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
[tex]A=\dfrac{1}{2}\times base\times height[/tex]
In a right angle triangle, the area of the triangle is
[tex]A=\dfrac{1}{2}\times leg_1\times leg_2[/tex]
Putting A=18 and [tex]leg_1=6[/tex], we get
[tex]18=\dfrac{1}{2}\times 6\times leg_2[/tex]
[tex]18=3\times leg_2[/tex]
Divide both sides by 3.
[tex]\dfrac{18}{3}=leg_2[/tex]
[tex]6=leg_2[/tex]
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.
