Question

A right triangle has an area of 18 square inches. Part 1 If the triangle is an isosceles triangle, what are the lengths of the legs of the triangle? The length of each leg is 6 inches. Part 2 out of 2 If the triangle is not an isosceles triangle, what are all the possible lengths of the legs? The possible lengths are_________.

Answer 1

The possible lengths are 2 x 18 , 3 x 12, 4x 9

Explanation:

Part 1) Given:

Area 'A'= 18 square inch

l=b=x (because isosceles triangle)

by the of equation of area of triangle

A = (1/2) (base) (height)

18 = (1/2) x . x

36 = x²

x²= 36

taking square root on both sides

x = 6 (The length of each leg is 6 inches.)

Part 2)

As area = 18, in above part we see that area before division must be 36, so lets find out the factor of 36.

36= 2 x 18

36= 3 x 12

36= 4x 9

Triangle have the dimension in the form of b x h

The possible lengths are , 2 x 18 , 3 x 12, 4x 9