Question

The legs of a right triangle are in the ratio 3 : 4 and its area is 1014 cm². Find the lengths of its legs.

Answer 1

In a right angled triangle, if one leg is the base, then the other leg is the height.
Let the given legs be 3x and 4x, respectively.
Area of the triangle = $\left(\frac{1}{2}\times 3x\times 4x\right)$ cm²
⇒ 1014 = (6x²)
⇒ 1014 = 6x²
⇒ x² = $\left(\frac{1014}{6}\right)$ = 169
⇒ x = $\sqrt{169}$ = 13
∴ Base = (3 $\times$ 13) = 39 cm
Height = (4 $\times$ 13) = 52 cm