A triangle has an area of 78 square inches and a height of 10.4 inches. What is the length of
the base?
inches

Question

A triangle has an area of 78 square inches and a height of 10.4 inches. What is the length of the base? inches

UpStudy AI · Accepted Answer

Given that the area $$ A $$ of a triangle is given by the formula

$$
A = \frac{1}{2} b h,
$$

where $$ b $$ is the base and $$ h $$ is the height, we can solve for $$ b $$ by rearranging the formula.

1. Substitute the known values $$ A = 78 $$ and $$ h = 10.4 $$:

$$
   78 = \frac{1}{2} b (10.4)
   $$

2. Multiply both sides by 2 to eliminate the fraction:

$$
   2 \times 78 = b \times 10.4 \quad \Rightarrow \quad 156 = 10.4b
   $$

3. Divide both sides by $$ 10.4 $$ to solve for $$ b $$:

$$
   b = \frac{156}{10.4}
   $$

4. Perform the division:

$$
   b = 15
   $$

Thus, the length of the base is $$ 15 $$ inches.
The base of the triangle is 15 inches.

Upstudy AI Solution