Multiple choice

The perimeter of right angled triangle is $24 cm$.If its hypotenuse is $10 $cm the area of this triangle is :

  1. $24 cm^2$
  2. $10 cm^2$
  3. $12 cm^2$
  4. $48 cm^2$
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A Correct answer
Explanation

Perimeter = a + b + c = 24. Hypotenuse c = 10. So a + b = 14. Also a^2 + b^2 = 100. (a+b)^2 = a^2 + b^2 + 2ab => 196 = 100 + 2ab => 2ab = 96 => ab = 48. Area = 1/2 * base * height = 1/2 * ab = 1/2 * 48 = 24.

AI explanation

The sum of the two legs is 24 cm minus the 10 cm hypotenuse, giving 14 cm. The square of this sum is 196, and subtracting the square of the hypotenuse, which is 100, leaves 96. Dividing 96 by 2 gives the product of the two legs as 48. The area of the right angled triangle is half of this product, so the area is 24 cm^2.

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