Multiple choice

The length of a rectangle is 1 cm more than its width and its perimeter is 14 cm then the area of the rectangle is

  1. $ \displaystyle 16 cm ^{2} $
  2. $ \displaystyle 14cm ^{2} $
  3. $ \displaystyle 12 cm ^{2} $
  4. $ \displaystyle 10 cm ^{2} $
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C Correct answer
Explanation

Let width = w, then length = w + 1. Perimeter = 2(l + w) = 2(w + 1 + w) = 14. So 2(2w + 1) = 14, which means 2w + 1 = 7, so 2w = 6, w = 3. Length = 4. Area = l * w = 4 * 3 = 12 cm^2.

AI explanation

Let the width be w cm, making the length (w + 1) cm; the rectangle perimeter formula gives 2 times the sum of length and width, so 2(w + w + 1) equals 14. Solving this equation yields a width of 3 cm and a length of 4 cm. Using the rectangle area formula, the area is 4 cm multiplied by 3 cm, resulting in 12 sq cm.

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