The hypotenuse of a right-angled triangle is more than one of the legs by 2. Find the lengths of the sides

The hypotenuse of a right-angled triangle is more than one of the legs by 2. Find the lengths of the sides of the triangle if its perimeter is 40.

It is known from the condition that the hypotenuse of a right-angled triangle is more than one of the legs by 2. Find the lengths of the sides of the triangle if its perimeter is 40.

We introduce the variable x – denoting the length of the leg, then the length of the hypotenuse can be written as (x + 2).

We also know the perimeter of the triangle and it is equal to the sum of the lengths of all sides of the triangle.

P = a + b + c;

x + x + 2 + c = 40;

c = 40 – 2 – 2x;

c = 38 – 2x is the length of the second leg.

Using the Pythagorean theorem, we compose and solve the equations.

a ^ 2 + b ^ 2 = c ^ 2;

The square of the hypotenuse is equal to the sum of the squares of the legs.

x ^ 2 + (38 – 2x) ^ 2 = (x + 2) ^ 2;

x ^ 2 + 1444 – 152x + 4x ^ 2 = x ^ 2 + 4x + 4;

4x ^ 2 – 156x + 1440 = 0;

x ^ 2 – 39x + 360 = 0;

D = 81;

x1 = 24; x2 = 15.

The first root does not fit because the perimeter is 40.

Leg 15; hypotenuse 15 + 2 = 17; second leg 38 – 2 * 15 = 38 – 30 = 8.