One of the legs of a right-angled triangle is 2 cm larger than the other. Find the legs if the hypotenuse is √37 cm

Let’s denote by x the length of the larger leg of this right-angled triangle.

According to the condition of the problem, one leg of this right-angled triangle is 2 cm larger than the other, therefore, the length of the smaller leg of this right-angled triangle is x – 2 cm.

It is also known that the hypotenuse of a given right-angled triangle is √37 cm, therefore, we can draw up the following equation:

x ^ 2 + (x – 2) ^ 2 = (√37) ^ 2.

We solve the resulting equation:

x ^ 2 + x ^ 2 – 4x + 4 = 37;

2x ^ 2 – 4x – 33 = 0;

x = (2 ± √ (4 + 33 * 2)) / 2 = (2 ± √70) / 2;

x = 1 + √70 / 2.

We find the second leg:

x – 2 = 1 + √70 / 2 – 2 = √70 / 2 – 1.

Answer: the legs of this right-angled triangle are 1 + √70 / 2 cm and √70 / 2 – 1 cm.