One leg of a right-angled triangle is 5 cm smaller than the other. Find the length of each leg if the area

One leg of a right-angled triangle is 5 cm smaller than the other. Find the length of each leg if the area of this triangle is 42 cm²

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 5 cm less than the other, therefore, the length of the smaller leg of this right-angled triangle is x – 5 cm.

It is also known that the area of ​​this triangle is 42 cm ^ 2, therefore, we can draw up the following equation:

x * (x – 5) / 2 = 42.

We solve the resulting equation:

x * (x – 5) = 84;

x ^ 2 – 5x – 84 = 0;

x = (5 ± √ (25 + 336)) / 2 = (5 ± 19) / 2;

x = (5 + 19) / 2 = 24/2 = 12 cm.

We find the second leg:

x – 5 = 12 – 5 = 7 cm.

Answer: the legs of this right-angled triangle are 7 cm and 12 cm.