208k views
13 votes
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?

User Kyron
by
6.6k points

1 Answer

10 votes

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

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


A=(1)/(2)* leg_1* leg_2

Putting A=18 and
leg_1=6, we get


18=(1)/(2)* 6* leg_2


18=3* leg_2

Divide both sides by 3.


(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.

User Binita Bharati
by
6.1k points