The perimeter of a right-angled triangle is 40 cm, and one of its legs is 15 cm. Find the area of the triangle.

The perimeter of a triangle is equal to the sum of its three sides. The first leg is known to us 15 cm, the length of the second leg is x cm, then the length of the hypotenuse is found as the difference between the perimeter and the sum of the lengths of the legs, i.e. 40 – (15 + x) = 40 – 15 – x = 25 – x (cm).

We apply the Pythagorean theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

(25 – x) ^ 2 = x ^ 2 + 15 ^ 2;

625 – 50x + x ^ 2 = x ^ 2 + 225;

-50x + x ^ 2 – x ^ 2 = 225 – 625;

-50x = -400;

x = -400: (-50);

x = 8 (cm) – second leg.

Find the area of ​​the triangle. The area of ​​a right-angled triangle is half the product of its legs. S = ab / 2.

S = (15 * 8) / 2 = 60 (cm ^ 2).

Answer. 60 cm ^ 2.