Question

An isosceles triangle has area of 105 ft2. If the base is 12 ft, what is the length of each leg? Round your answer to the nearest tenth.
A) 450.3 ft
B) 14.5 ft
C) 21.2 ft
D) 18.5 ft

Answer 1

Answer: Option D) 18.5 ft

Solution:
Area of the isosceles triangle: A=105 ft^2
Base of the isosceles triangle: B=12 ft
Length of each leg of the isosceles triangle: L=?

A=BH/2
Height of the isosceles triangle (perpendicular to the base): H=?

Replacing the known values in the formula of Area:
105 ft^2=(12 ft)H/2
105 ft^2=(6 ft)H

Solving for H: Dividing both sides by 6 ft:
(105 ft^2)/(6 ft)=(6 ft)H/(6 ft)
17.5 ft=H
H=17.5 ft

Using the Pytagoras Theorem:
c^2=a^2+b^2
with:
c=L=?
a=B/2=(12 ft)/2→a=6 ft
b=H→b=17.5 ft

L^2=(6 ft)^2+(17.5)^2
L^2=36 ft^2+306.25 ft^2
L^2=342.25 ft^2
sqrt(L^2)=sqrt(342.25 ft^2)
L=18.5 ft

Answer: The length of each leg is 18.5 ft