Question

A right triangle has an area of 18 The length of each leg is 6 inches. If the triangle is not an isosceles triangle, what are all the possible lengths of the legs?

Answer 1

Given:

Area of a right triangle = 18 sq. inches

Length of one leg = 6 inches

To find:

The length of another leg.

Solution:

We know that, the area of a triangle is

$A=\dfrac{1}{2}\times base\times height$

In a right angle triangle, the area of the triangle is

$A=\dfrac{1}{2}\times leg_1\times leg_2$

Putting A=18 and $leg_1=6$, we get

$18=\dfrac{1}{2}\times 6\times leg_2$

$18=3\times leg_2$

Divide both sides by 3.

$\dfrac{18}{3}=leg_2$

$6=leg_2$

Both legs are equal so the given triangle is an isosceles right triangle.

If the triangle is not isosceles triangle, then the length of legs are factors of 36 because half of 36 is 18.

Therefore, the possible pairs of legs are 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6, 9 and 4, 12 and 3, 18 and 2, 36 and 1.