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