Multiple choice

What is the area (in sq. cm) of a rectangle, if its diagonal is 25 cm and one of its sides is 24 cm?

  1. 186

  2. 144

  3. 132

  4. 168
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D Correct answer
Explanation

In a rectangle, diagonal^2 = side1^2 + side2^2. 25^2 = 24^2 + side2^2 => 625 = 576 + side2^2 => side2^2 = 49 => side2 = 7. Area = 24 * 7 = 168.

AI explanation

The diagonal of a rectangle forms a right triangle with its two adjacent sides, so we use the Pythagorean theorem to find the unknown side. Let the unknown side be x, giving the equation 24^2 + x^2 = 25^2, which yields 576 + x^2 = 625 and x = 7 centimeters. The area of the rectangle is length times width, so multiplying 24 by 7 gives an area of 168 square centimeters.

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