The area of a right-angled triangle is 168 cm2. Find his legs if the ratio of their lengths is 7/12

The area of a right-angled triangle is s = ½ * a * b, where a and b, respectively, are the legs of the triangle.

S = 168 cm2.

The legs are in the ratio a / b = 7/12, then a = 7/12 * b. Substitute in the area

168 = ½ * 7/12 * b * b;

168 = 7/24 * b ^ 2;

b ^ 2 = 168: 7/24;

b ^ 2 = 576;

b = 24;

One leg is 24 cm, then the other is a = 7/12 * 24 = 14 cm.