An isosceles triangle has an area of 150 ft2. If the base is 12 ft, what is the length of each leg? Round the answer to the nearest tenth.
Solution:
Given, area of isosceles triangle = 150 square feet.
Base of the triangle = 12 ft
We have to find the length of each leg.
The side length can be found by using Pythagorean theorem,
a2 = (b/2)2 + h2
a2 = (12/2)2 + h2
The height ‘h’ can be computed using the given area.
Area = (base × height)/2
150 = 12(h)/2
150 = 6h
h = 150/6
h = 25 ft
Put the value of h in Pythagorean theorem,
a2 = (6)2 + (25)2
a2 = 36 + 625
a2 = 661
Taking square root,
a = √661
a = 25.71 ≈ 25
Therefore, the length of each leg is 25 ft.
An isosceles triangle has an area of 150 ft2. If the base is 12 ft, what is the length of each leg? Round the answer to the nearest tenth.
Summary:
An isosceles triangle has an area of 150 ft2. If the base is 12 ft, the length of each leg is 25 ft.