Question

the length of the hypotenuse of an isoceles right triangle with area 72cm²​

Answer 1

$\frac{1}{2} bh = {72cm}^{2} \\ base = height(isosceles \: triangle)$

$\frac{1}{2} {b}^{2} = 72 \\ {b}^{2} = 144 \\ b = \sqrt{144} = 12cm \\ h = 12cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Using pythagoras theorem

$hypotenuse = \sqrt{ {b}^{2} + {h}^{2} } = \sqrt{ {12}^{2} + {12 }^{2} } = \sqrt{144 + 144} = \sqrt{288} = 12 \sqrt{2}$