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The perimeter of a rectangle, whose length is 6 metre more than its breadth, is 84 metre. What is the area of the triangle whose base is equal to the diagonal of the rectangle and height is equal to the length of the rectangle?
- a)390 sq. metre
- b)360 sq. metre
- c)380 sq. metre
- d)400 sq. metre
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The perimeter of a rectangle, whose length is 6 metre more than its br...
Perimeter of the rectangle = 2(l + b) = 84
⇒ 2(b + b + 6) = 84
⇒ 2b + 6 = 42
⇒ b = 18 m
Thus, length = 24 m
Since 18 and 24, when divided by 6, give 3 and 4, respectively, they would be the sides of a right triangle with triplets as 3, 4, 5 or 18, 24, 30.
Thus, diagonal of the rectangle = 30 m
Area of the required
=
⇒ 2(b + b + 6) = 84
⇒ 2b + 6 = 42
⇒ b = 18 m
Thus, length = 24 m
Since 18 and 24, when divided by 6, give 3 and 4, respectively, they would be the sides of a right triangle with triplets as 3, 4, 5 or 18, 24, 30.
Thus, diagonal of the rectangle = 30 m
Area of the required
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Community Answer
The perimeter of a rectangle, whose length is 6 metre more than its br...
Given:
Perimeter of the rectangle = 84 meters
Let's assume:
Breadth of the rectangle = x meters
Length of the rectangle = x + 6 meters
Perimeter of the rectangle is given by the formula:
Perimeter = 2 × (Length + Breadth)
So, substituting the given values:
84 = 2 × (x + (x + 6))
Simplifying the equation:
84 = 2 × (2x + 6)
84 = 4x + 12
4x = 84 - 12
4x = 72
x = 72/4
x = 18
Therefore, the breadth of the rectangle is 18 meters and the length is 18 + 6 = 24 meters.
Finding the Diagonal of the Rectangle:
The diagonal of a rectangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The diagonal of the rectangle is the hypotenuse of a right-angled triangle, where the length and breadth of the rectangle are the other two sides.
Using the formula:
Diagonal^2 = Length^2 + Breadth^2
Substituting the given values:
Diagonal^2 = 24^2 + 18^2
Diagonal^2 = 576 + 324
Diagonal^2 = 900
Diagonal = √900
Diagonal = 30 meters
Finding the Area of the Triangle:
The area of a triangle can be calculated using the formula:
Area = (1/2) × Base × Height
Given:
Base = Diagonal = 30 meters
Height = Length of the rectangle = 24 meters
Substituting the values:
Area = (1/2) × 30 × 24
Area = 360 square meters
Therefore, the area of the triangle is 360 square meters. Hence, option B is the correct answer.
Perimeter of the rectangle = 84 meters
Let's assume:
Breadth of the rectangle = x meters
Length of the rectangle = x + 6 meters
Perimeter of the rectangle is given by the formula:
Perimeter = 2 × (Length + Breadth)
So, substituting the given values:
84 = 2 × (x + (x + 6))
Simplifying the equation:
84 = 2 × (2x + 6)
84 = 4x + 12
4x = 84 - 12
4x = 72
x = 72/4
x = 18
Therefore, the breadth of the rectangle is 18 meters and the length is 18 + 6 = 24 meters.
Finding the Diagonal of the Rectangle:
The diagonal of a rectangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The diagonal of the rectangle is the hypotenuse of a right-angled triangle, where the length and breadth of the rectangle are the other two sides.
Using the formula:
Diagonal^2 = Length^2 + Breadth^2
Substituting the given values:
Diagonal^2 = 24^2 + 18^2
Diagonal^2 = 576 + 324
Diagonal^2 = 900
Diagonal = √900
Diagonal = 30 meters
Finding the Area of the Triangle:
The area of a triangle can be calculated using the formula:
Area = (1/2) × Base × Height
Given:
Base = Diagonal = 30 meters
Height = Length of the rectangle = 24 meters
Substituting the values:
Area = (1/2) × 30 × 24
Area = 360 square meters
Therefore, the area of the triangle is 360 square meters. Hence, option B is the correct answer.
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The perimeter of a rectangle, whose length is 6 metre more than its breadth, is 84 metre. What is the area of the triangle whose base is equal to the diagonal of the rectangle and height is equal to the length of the rectangle?a)390 sq. metreb)360 sq. metrec)380 sq. metred)400 sq. metreCorrect answer is option 'B'. Can you explain this answer?
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The perimeter of a rectangle, whose length is 6 metre more than its breadth, is 84 metre. What is the area of the triangle whose base is equal to the diagonal of the rectangle and height is equal to the length of the rectangle?a)390 sq. metreb)360 sq. metrec)380 sq. metred)400 sq. metreCorrect answer is option 'B'. 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 The perimeter of a rectangle, whose length is 6 metre more than its breadth, is 84 metre. What is the area of the triangle whose base is equal to the diagonal of the rectangle and height is equal to the length of the rectangle?a)390 sq. metreb)360 sq. metrec)380 sq. metred)400 sq. metreCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of a rectangle, whose length is 6 metre more than its breadth, is 84 metre. What is the area of the triangle whose base is equal to the diagonal of the rectangle and height is equal to the length of the rectangle?a)390 sq. metreb)360 sq. metrec)380 sq. metred)400 sq. metreCorrect answer is option 'B'. Can you explain this answer?.
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