# The height of a triangle is twice it's base and the area is 576 square inches . What is the length of the base?

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### 3 Answers

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

We'll simplify:

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.**