Multiple choice

The length of a rectangle is $\displaystyle \left( \frac{3}{4} \right)^{th}$ of its breadth. If its perimeter is 126 m, then its area will be _______.

  1. 972 $m^2$
  2. 640 $m^2$
  3. 840 $m^2$
  4. 954 $m^2$
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A Correct answer
Explanation

Length L = 3/4 * B. Perimeter = 2(L + B) = 2(3/4B + B) = 2(7/4B) = 7/2B = 126. B = 126 * 2 / 7 = 36. L = 3/4 * 36 = 27. Area = L * B = 27 * 36 = 972 m^2.

AI explanation

Let the breadth be x, making the length 3x divided by 4. The perimeter formula 2 times length plus breadth gives 2 times the sum of 3x divided by 4 and x, which equals 126. Solving 7x divided by 2 equals 126 yields x equals 36, meaning the sides are 27 m and 36 m. The area is 27 times 36, which equals 972 m squared.

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