Multiple choice

The length of a rectangle is $\left( \cfrac { 6 }{ 5 } \right) $th of its breadth. It its perimeter is $132m$, its area will be ______ .

  1. $1080{m}^{2}$
  2. $640{m}^{2}$
  3. $1620{m}^{2}$
  4. $2160{m}^{2}$
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A Correct answer
Explanation

Let the breadth be b, so the length is 6b/5. From the perimeter, 2(6b/5 + b) = 132, giving b = 30 m and length = 36 m. The area is 36 x 30 = 1080 m^2.

AI explanation

Let the breadth be x, making the length 6 over 5 times x, and apply the rectangle perimeter formula: 2 times length plus breadth equals 132. This gives 2 times 6 over 5 x plus x equals 132, which simplifies to 22 over 5 x equals 132, yielding a breadth of 30 meters. The length is 36 meters, and applying the rectangle area formula of length times breadth gives an area of 1080 square meters.

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