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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