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The area of a rectangle is equal to the area of a square whose diagonal is 12√6 metre. The difference between the length and the breadth of the rectangle is 6 metre. What is the perimeter of rectangle ? (in metre).
- a)160 metre
- b)80 metre
- c)82 metre
- d)84 metre
- e)None of the Above
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The area of a rectangle is equal to the area of a square whose diagona...
d = a√2
12√6 = a√2
a = 12√3 l * b = a² = (12√3)² = 432
l – b = 6 ; l = b + 6
(b + 6)*(b) = 432
b² + 6b – 432 = 0
b = 18; l = 24
2(l + b) = 2(24 + 18) = 84m
12√6 = a√2
a = 12√3 l * b = a² = (12√3)² = 432
l – b = 6 ; l = b + 6
(b + 6)*(b) = 432
b² + 6b – 432 = 0
b = 18; l = 24
2(l + b) = 2(24 + 18) = 84m
Most Upvoted Answer
The area of a rectangle is equal to the area of a square whose diagona...
d = a√2
12√6 = a√2
a = 12√3 l * b = a² = (12√3)² = 432
l – b = 6 ; l = b + 6
(b + 6)*(b) = 432
b² + 6b – 432 = 0
b = 18; l = 24
2(l + b) = 2(24 + 18) = 84m
12√6 = a√2
a = 12√3 l * b = a² = (12√3)² = 432
l – b = 6 ; l = b + 6
(b + 6)*(b) = 432
b² + 6b – 432 = 0
b = 18; l = 24
2(l + b) = 2(24 + 18) = 84m
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The area of a rectangle is equal to the area of a square whose diagona...
Given Information:
- The area of a rectangle is equal to the area of a square whose diagonal is 12√6 meters.
- The difference between the length and breadth of the rectangle is 6 meters.
Solution:
To solve this problem, we need to find the length and breadth of the rectangle and then calculate its perimeter.
Finding the Length and Breadth of the Rectangle:
Let the length of the rectangle be 'l' meters and the breadth be 'b' meters.
Given that the area of the rectangle is equal to the area of a square with diagonal 12√6 meters:
Area of rectangle = l * b
Area of square = (side)^2 = (diagonal/sqrt(2))^2 = (12√6/sqrt(2))^2 = 72 * 6 = 432 square meters
Therefore, l * b = 432
Given that the difference between length and breadth is 6 meters:
l - b = 6
Solving these two equations simultaneously, we get:
l = 24 meters
b = 18 meters
Calculating the Perimeter of the Rectangle:
Perimeter of a rectangle = 2(l + b)
= 2(24 + 18)
= 2 * 42
= 84 meters
Therefore, the perimeter of the rectangle is 84 meters, which corresponds to option 'D'.
- The area of a rectangle is equal to the area of a square whose diagonal is 12√6 meters.
- The difference between the length and breadth of the rectangle is 6 meters.
Solution:
To solve this problem, we need to find the length and breadth of the rectangle and then calculate its perimeter.
Finding the Length and Breadth of the Rectangle:
Let the length of the rectangle be 'l' meters and the breadth be 'b' meters.
Given that the area of the rectangle is equal to the area of a square with diagonal 12√6 meters:
Area of rectangle = l * b
Area of square = (side)^2 = (diagonal/sqrt(2))^2 = (12√6/sqrt(2))^2 = 72 * 6 = 432 square meters
Therefore, l * b = 432
Given that the difference between length and breadth is 6 meters:
l - b = 6
Solving these two equations simultaneously, we get:
l = 24 meters
b = 18 meters
Calculating the Perimeter of the Rectangle:
Perimeter of a rectangle = 2(l + b)
= 2(24 + 18)
= 2 * 42
= 84 meters
Therefore, the perimeter of the rectangle is 84 meters, which corresponds to option 'D'.
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