Multiple choice

An isosceles right-angled triangle has area $200:cm^{2}$ What is the length of its hypotenuse $?$

  1. $\displaystyle 20\sqrt{2}$ cm
  2. $\displaystyle 30\sqrt{2}$ cm
  3. $\displaystyle 70\sqrt{2}$ cm
  4. $\displaystyle 80\sqrt{2}$ cm
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A Correct answer
Explanation

Area of isosceles right triangle = (1/2) * side^2 = 200, so side^2 = 400, side = 20. Hypotenuse = sqrt(side^2 + side^2) = sqrt(400 + 400) = sqrt(800) = 20 * sqrt(2).

AI explanation

Using the area formula for a right isosceles triangle with equal sides a, the area is a squared divided by 2. Setting this equal to 200 cm squared gives a squared equals 400, so a equals 20 cm. Using the Pythagorean theorem, the hypotenuse is a times the square root of 2, which is 20 times the square root of 2 cm.

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