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A wire which was used to form a square of side 30 cm is divided into 3 parts such that the length of the longest part is 25% more than length of the second longest part. If the shortest part is 20 cm shorter than the longest part, then the area (in cm2) of the triangle formed by these three parts is
- a)540
- b)480
- c)800
- d)600
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A wire which was used to form a square of side 30 cm is divided into 3...
The length of the wire = 4*30 = 120 cm.
Let 'x' be the length of the smallest part of the wire.
Length of the longest part = x + 20
Length of the second longest part*1.25 = Length of the longest part
⇒ Length of the second longest part = 0.8*Length of the longest part
⇒ x + 20 + 0.8*(x+20) + x = 120
⇒ x + 20 + 0.8x + 16 + x = 120
2.8x + 36 = 120
2.8x = 84
⇒ x = 30 cm
The sides of the triangle are 30 cm, 40 cm, and 50 cm.
We can see that the sides of the triangle form a Pythagorean triplet.
Therefore, the area of the triangle is 0.5*30*40 = 600 cm2
Therefore, option D is the right answer.
Let 'x' be the length of the smallest part of the wire.
Length of the longest part = x + 20
Length of the second longest part*1.25 = Length of the longest part
⇒ Length of the second longest part = 0.8*Length of the longest part
⇒ x + 20 + 0.8*(x+20) + x = 120
⇒ x + 20 + 0.8x + 16 + x = 120
2.8x + 36 = 120
2.8x = 84
⇒ x = 30 cm
The sides of the triangle are 30 cm, 40 cm, and 50 cm.
We can see that the sides of the triangle form a Pythagorean triplet.
Therefore, the area of the triangle is 0.5*30*40 = 600 cm2
Therefore, option D is the right answer.
Most Upvoted Answer
A wire which was used to form a square of side 30 cm is divided into 3...
Given:
- A wire is used to form a square of side 30 cm.
- The wire is divided into 3 parts.
- The length of the longest part is 25% more than the length of the second longest part.
- The shortest part is 20 cm shorter than the longest part.
To find:
- The area of the triangle formed by these three parts.
Solution:
Let the length of the second longest part be x cm.
According to the given information:
- The length of the longest part = x + 25% of x = x + (25/100)x = (5/4)x
- The shortest part = length of the longest part - 20 cm = (5/4)x - 20 cm
Since the wire is used to form a square of side 30 cm, the sum of the lengths of the three parts should be equal to the perimeter of the square.
Perimeter of the square = 4 * side = 4 * 30 cm = 120 cm
Therefore, we can write the equation as:
x + (5/4)x + (5/4)x - 20 = 120
Simplifying the equation:
(9/4)x - 20 = 120
(9/4)x = 140
x = (4/9) * 140
x = 62.22 cm (approx)
Calculating the lengths of the three parts:
Length of the second longest part = x = 62.22 cm (approx)
Length of the longest part = (5/4)x = (5/4) * 62.22 cm = 77.78 cm (approx)
Length of the shortest part = (5/4)x - 20 = 77.78 - 20 = 57.78 cm (approx)
Calculating the area of the triangle:
To find the area of the triangle, we need the lengths of its three sides.
Using Heron's formula, the area of a triangle with sides a, b, and c is given by:
Area = √(s(s-a)(s-b)(s-c))
Where s is the semi-perimeter of the triangle.
Semi-perimeter, s = (a + b + c)/2
Substituting the values of a, b, and c:
Semi-perimeter, s = (62.22 + 77.78 + 57.78)/2 = 97.39 cm (approx)
Area = √(97.39(97.39-62.22)(97.39-77.78)(97.39-57.78))
= √(97.39 * 35.17 * 19.61 * 39.61)
= √(135,634.11)
= 368.40 cm² (approx)
Therefore, the area of the triangle formed by the three parts is approximately 368.40 cm², which is not given as an option. So, the correct answer cannot be determined from the given options.
- A wire is used to form a square of side 30 cm.
- The wire is divided into 3 parts.
- The length of the longest part is 25% more than the length of the second longest part.
- The shortest part is 20 cm shorter than the longest part.
To find:
- The area of the triangle formed by these three parts.
Solution:
Let the length of the second longest part be x cm.
According to the given information:
- The length of the longest part = x + 25% of x = x + (25/100)x = (5/4)x
- The shortest part = length of the longest part - 20 cm = (5/4)x - 20 cm
Since the wire is used to form a square of side 30 cm, the sum of the lengths of the three parts should be equal to the perimeter of the square.
Perimeter of the square = 4 * side = 4 * 30 cm = 120 cm
Therefore, we can write the equation as:
x + (5/4)x + (5/4)x - 20 = 120
Simplifying the equation:
(9/4)x - 20 = 120
(9/4)x = 140
x = (4/9) * 140
x = 62.22 cm (approx)
Calculating the lengths of the three parts:
Length of the second longest part = x = 62.22 cm (approx)
Length of the longest part = (5/4)x = (5/4) * 62.22 cm = 77.78 cm (approx)
Length of the shortest part = (5/4)x - 20 = 77.78 - 20 = 57.78 cm (approx)
Calculating the area of the triangle:
To find the area of the triangle, we need the lengths of its three sides.
Using Heron's formula, the area of a triangle with sides a, b, and c is given by:
Area = √(s(s-a)(s-b)(s-c))
Where s is the semi-perimeter of the triangle.
Semi-perimeter, s = (a + b + c)/2
Substituting the values of a, b, and c:
Semi-perimeter, s = (62.22 + 77.78 + 57.78)/2 = 97.39 cm (approx)
Area = √(97.39(97.39-62.22)(97.39-77.78)(97.39-57.78))
= √(97.39 * 35.17 * 19.61 * 39.61)
= √(135,634.11)
= 368.40 cm² (approx)
Therefore, the area of the triangle formed by the three parts is approximately 368.40 cm², which is not given as an option. So, the correct answer cannot be determined from the given options.
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Community Answer
A wire which was used to form a square of side 30 cm is divided into 3...
The length of the wire = 4*30 = 120 cm.
Let 'x' be the length of the smallest part of the wire.
Length of the longest part = x + 20
Length of the second longest part*1.25 = Length of the longest part
⇒ Length of the second longest part = 0.8*Length of the longest part
⇒ x + 20 + 0.8*(x+20) + x = 120
⇒ x + 20 + 0.8x + 16 + x = 120
2.8x + 36 = 120
2.8x = 84
⇒ x = 30 cm
The sides of the triangle are 30 cm, 40 cm, and 50 cm.
We can see that the sides of the triangle form a Pythagorean triplet.
Therefore, the area of the triangle is 0.5*30*40 = 600 cm2
Therefore, option D is the right answer.
Let 'x' be the length of the smallest part of the wire.
Length of the longest part = x + 20
Length of the second longest part*1.25 = Length of the longest part
⇒ Length of the second longest part = 0.8*Length of the longest part
⇒ x + 20 + 0.8*(x+20) + x = 120
⇒ x + 20 + 0.8x + 16 + x = 120
2.8x + 36 = 120
2.8x = 84
⇒ x = 30 cm
The sides of the triangle are 30 cm, 40 cm, and 50 cm.
We can see that the sides of the triangle form a Pythagorean triplet.
Therefore, the area of the triangle is 0.5*30*40 = 600 cm2
Therefore, option D is the right answer.
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A wire which was used to form a square of side 30 cm is divided into 3 parts such that the length of the longest part is 25% more than length of the second longest part. If the shortest part is 20 cm shorter than the longest part, then the area (in cm2) of the triangle formed by these three parts isa)540b)480c)800d)600Correct answer is option 'D'. Can you explain this answer?
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A wire which was used to form a square of side 30 cm is divided into 3 parts such that the length of the longest part is 25% more than length of the second longest part. If the shortest part is 20 cm shorter than the longest part, then the area (in cm2) of the triangle formed by these three parts isa)540b)480c)800d)600Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A wire which was used to form a square of side 30 cm is divided into 3 parts such that the length of the longest part is 25% more than length of the second longest part. If the shortest part is 20 cm shorter than the longest part, then the area (in cm2) of the triangle formed by these three parts isa)540b)480c)800d)600Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire which was used to form a square of side 30 cm is divided into 3 parts such that the length of the longest part is 25% more than length of the second longest part. If the shortest part is 20 cm shorter than the longest part, then the area (in cm2) of the triangle formed by these three parts isa)540b)480c)800d)600Correct answer is option 'D'. Can you explain this answer?.
A wire which was used to form a square of side 30 cm is divided into 3 parts such that the length of the longest part is 25% more than length of the second longest part. If the shortest part is 20 cm shorter than the longest part, then the area (in cm2) of the triangle formed by these three parts isa)540b)480c)800d)600Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A wire which was used to form a square of side 30 cm is divided into 3 parts such that the length of the longest part is 25% more than length of the second longest part. If the shortest part is 20 cm shorter than the longest part, then the area (in cm2) of the triangle formed by these three parts isa)540b)480c)800d)600Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire which was used to form a square of side 30 cm is divided into 3 parts such that the length of the longest part is 25% more than length of the second longest part. If the shortest part is 20 cm shorter than the longest part, then the area (in cm2) of the triangle formed by these three parts isa)540b)480c)800d)600Correct answer is option 'D'. Can you explain this answer?.
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