# Find the hypotenuse of an isosceles right-angled triangle if its area is 18 cm2.

August 25, 2021 | education

| The area of a right-angled triangle is equal to half the product of its legs:

S = 0.5 * a * b.

In an isosceles right-angled triangle, the legs are equal to each other, which means the area is: S = 0.5 * a ^ 2.

Hence, a ^ 2 = 2 * S = 2 * 18 = 36;

The legs of this triangle are equal: a = √36 = 6 cm.

By the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypotenuse: a ^ 2 + b ^ 2 = c ^ 2.

For an isosceles right triangle: a ^ 2 + a ^ 2 = c ^ 2;

Hence, the hypotenuse is equal to: c = √ (6 ^ 2 + 6 ^ 2) = √ (36 + 36) = 6√2 ≈ 8.49 cm.

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