The height of a triangle is twice it's base and the area is 576 square inches . What is the length of the base?
The area of a triangle is given as (1/2)*base*height.
Now in the given triangle, the height is twice the base and the area is 576
=> (1/2)* base*2*base = 576
=> base^2 = 576
=> base = 24
Therefore the base is 24 inches.
The area A of the triangle A = (1/2) bh, where b is base of the triangle and h is the height of the triangle.
Given h = 2b...(1) and A = (1/2)bh = 576 sq inch.
Therefore from bh = 2*576 = 1152. we put h = 2b in bh = 1152:
b*2b = 1152.
2b^2 = 1152.
b ^2 = 1152/2 = 576.
b = sqrt(576) = 24.
So h = 2b = 2* 24 = 48 in.
Therefore base = b = 24 in.
First, we'll recall the formula of the area of a triangle, that contains the base and the height.
A = b*h/2 (1)
b = base
h = height
From enunciation, we have that:
h = 2b (2)
We'll substitute (2) in (1) and we'll get:
A = b*2b/2
A = b^2
From enunciation, the value of the area is:
576 square inches = b^2
We'll take square root both sides:
sqrt 576 = sqrt b^2
b = 24 inches
The length of the base of triangle is b = 24 inches long.