One of the legs = 7 cm. The hypotenuse is 5 cm larger than the second leg. Calculate the perimeter.

From the condition it is known that one of the legs is 7 cm, and it is also known that the hypotenuse is 5 cm larger than the second leg.To calculate the perimeter of the triangle, we use the formula:

P = a + b + c;

To find the hypotenuse and leg of a triangle, we will apply the Pythagorean theorem. Let’s denote by x cm – the length of the second leg, then (x + 5) cm is the length of the hypotenuse.

We apply the Pythagorean theorem and get the equation:

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

(x + 5) ^ 2 = x ^ 2 + 7 ^ 2;

x ^ 2 + 10x + 25 = x ^ 2 + 49;

x ^ 2 – x ^ 2 + 10x = 49 – 25;

10x = 24;

x = 2.4 cm leg, and 2.4 + 5 = 7.4 cm hypotenuse length.

P = 7 + 2.4 + 7.4 = 16.8 cm.