Question

The legs of a right triangle are in the ratio 3:4 and its area is 1014 CM square find the length of its legs

Answer 1

Let the common ratio be x.

Therefore, one leg = 3x cm and the other leg = 4x cm

Area of the triangle = 1/2 × 3x × 4x

or, 1014 = 6x²

or, x² = 1014/6 = 169

or, x = √169 = ± 13

We will consider the positive value here, i.e., x = + 13 and moreover, in this case x cannot bear a negative value.

So, Length of one leg = (3×13) cm = 39 cm

Length of other leg = (4×13) cm = 52 cm