# The area of a right-angled triangle is 18 cm ^ 2. The square of the length of its hypotenuse is 97 cm ^ 2

October 12, 2021 | education

| **The area of a right-angled triangle is 18 cm ^ 2. The square of the length of its hypotenuse is 97 cm ^ 2. What is the sum of the lengths of the legs of this triangle? Make up a system of equations to solve the problem)**

Let’s introduce variables.

Let m be the length of one leg of the triangle, n the length of the second leg.

The area of a triangle is the product of the legs, divided by two.

S = 1/2 * m * n;

18 = 1/2 * m * n;

m * n = 36;

By the Pythagorean theorem, we get:

m ^ 2 + n ^ 2 = 97;

We get a system of two equations with two unknowns:

m * n = 36;

m ^ 2 + n ^ 2 = 97;

Let’s use the method of algebraic addition – add the second equation and the first, multiplied by two:

m ^ 2 + n ^ 2 + 2 * m * n = 97 + 72;

(m + n) ^ 2 = 169;

m + n = 13 cm.

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