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Smallest side of a right-angled triangle is 13 cm less than the side of a square of perimeter 72 cm. The second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm.
Quantity I: Six more than the side of the right-angled triangle(not the smallest)
Quantity II: The Sum of Hypotenuse of the right-angled triangle and the smallest side
Quantity II: The Sum of Hypotenuse of the right-angled triangle and the smallest side
- a)Quantity I > Quantity II
- b)Quantity I < Quantity II
- c)Quantity I ≥ Quantity II
- d)Quantity I ≤ Quantity II
- e)Quantity I = Quantity II or relation cannot be established
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
Smallest side of a right-angled triangle is 13 cm less than the side o...
Side of square = 72/4 = 18 cm
Smallest side of the right angled triangle = 18 – 13 = 5 cm
Length of rectangle = 112/8 = 14 cm
Second side of the right angled triangle = 14 – 2 = 12 cm
Hypotenuse of the right angled triangle = √(25 + 144) = 13cm
Smallest side of the right angled triangle = 18 – 13 = 5 cm
Length of rectangle = 112/8 = 14 cm
Second side of the right angled triangle = 14 – 2 = 12 cm
Hypotenuse of the right angled triangle = √(25 + 144) = 13cm
Most Upvoted Answer
Smallest side of a right-angled triangle is 13 cm less than the side o...
Let's solve this step by step.
Let's assume the side of the square is x cm.
The perimeter of the square is 4x cm.
According to the problem, 4x = 72 cm.
Dividing both sides by 4, we get x = 18 cm.
The smallest side of the right-angled triangle is 13 cm less than the side of the square.
Therefore, the smallest side of the right-angled triangle is 18 - 13 = 5 cm.
Let's assume the length of the rectangle is y cm.
The area of the rectangle is y * width = 112 cm.
The width of the rectangle is 112 / y cm.
The second largest side of the right-angled triangle is 2 cm less than the length of the rectangle.
Therefore, the second largest side of the right-angled triangle is y - 2 cm.
So, the sides of the right-angled triangle are 5 cm, y - 2 cm, and 112 / y cm.
Since it is a right-angled triangle, we can use the Pythagorean theorem to find the third side.
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Therefore, (5 cm)^2 + (y - 2 cm)^2 = (112 / y cm)^2.
Expanding this equation, we get:
25 + y^2 - 4y + 4 = 12544 / y^2.
Simplifying this equation, we get:
y^4 - 4y^3 + 4y^2 + 12544 = 25y^2.
Bringing all terms to one side, we get:
y^4 - 4y^3 - 21y^2 + 12544 = 0.
This is a quartic equation that can be solved using various methods such as factoring, using the Rational Root Theorem, or using numerical methods.
Unfortunately, solving this equation will require more information or the use of advanced mathematical methods.
Let's assume the side of the square is x cm.
The perimeter of the square is 4x cm.
According to the problem, 4x = 72 cm.
Dividing both sides by 4, we get x = 18 cm.
The smallest side of the right-angled triangle is 13 cm less than the side of the square.
Therefore, the smallest side of the right-angled triangle is 18 - 13 = 5 cm.
Let's assume the length of the rectangle is y cm.
The area of the rectangle is y * width = 112 cm.
The width of the rectangle is 112 / y cm.
The second largest side of the right-angled triangle is 2 cm less than the length of the rectangle.
Therefore, the second largest side of the right-angled triangle is y - 2 cm.
So, the sides of the right-angled triangle are 5 cm, y - 2 cm, and 112 / y cm.
Since it is a right-angled triangle, we can use the Pythagorean theorem to find the third side.
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Therefore, (5 cm)^2 + (y - 2 cm)^2 = (112 / y cm)^2.
Expanding this equation, we get:
25 + y^2 - 4y + 4 = 12544 / y^2.
Simplifying this equation, we get:
y^4 - 4y^3 + 4y^2 + 12544 = 25y^2.
Bringing all terms to one side, we get:
y^4 - 4y^3 - 21y^2 + 12544 = 0.
This is a quartic equation that can be solved using various methods such as factoring, using the Rational Root Theorem, or using numerical methods.
Unfortunately, solving this equation will require more information or the use of advanced mathematical methods.
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Smallest side of a right-angled triangle is 13 cm less than the side of a square of perimeter 72 cm. The second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm.Quantity I: Six more than the side of the right-angled triangle(not the smallest)Quantity II: The Sum of Hypotenuse of the right-angled triangle and the smallest sidea)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer?
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Smallest side of a right-angled triangle is 13 cm less than the side of a square of perimeter 72 cm. The second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm.Quantity I: Six more than the side of the right-angled triangle(not the smallest)Quantity II: The Sum of Hypotenuse of the right-angled triangle and the smallest sidea)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Smallest side of a right-angled triangle is 13 cm less than the side of a square of perimeter 72 cm. The second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm.Quantity I: Six more than the side of the right-angled triangle(not the smallest)Quantity II: The Sum of Hypotenuse of the right-angled triangle and the smallest sidea)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Smallest side of a right-angled triangle is 13 cm less than the side of a square of perimeter 72 cm. The second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm.Quantity I: Six more than the side of the right-angled triangle(not the smallest)Quantity II: The Sum of Hypotenuse of the right-angled triangle and the smallest sidea)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer?.
Smallest side of a right-angled triangle is 13 cm less than the side of a square of perimeter 72 cm. The second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm.Quantity I: Six more than the side of the right-angled triangle(not the smallest)Quantity II: The Sum of Hypotenuse of the right-angled triangle and the smallest sidea)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Smallest side of a right-angled triangle is 13 cm less than the side of a square of perimeter 72 cm. The second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm.Quantity I: Six more than the side of the right-angled triangle(not the smallest)Quantity II: The Sum of Hypotenuse of the right-angled triangle and the smallest sidea)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Smallest side of a right-angled triangle is 13 cm less than the side of a square of perimeter 72 cm. The second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm.Quantity I: Six more than the side of the right-angled triangle(not the smallest)Quantity II: The Sum of Hypotenuse of the right-angled triangle and the smallest sidea)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer?.
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