In a right-angled triangle, one leg is 3 centimeters longer than the other and the area is 18. Find the length of the hypotenuse.

univerkov | April 3, 2021 | education

Let’s designate one leg as x, and the second leg as x + 3 cm. Their product is equal to two areas of the triangle. Let’s make an equation.

x * (x + 3) = 18 * 2.

x² + 3 * x = 36.

x² + 3 * x – 36 = 0.

D = 9 + 144 = 153.

x1 = (-3 + √153) ÷ 2 = 4.68.

x2 = (-3 – √153) ÷ 2 = -7.68.

One leg is 4.68 cm, the second 7.68 cm.Let’s find the hypotenuse.

s = √ ((7.68 cm) ² + (4.68 cm) ²) = 9 cm.

Answer: The hypotenuse is 9 cm.

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