Question

What is the height of a triangle with area $67.5$ square meters and base $9$ meters?

Short answer

The height of the triangle is$15$meters.

Step-by-step solution

Step 1. Given Information

It is given that the area of a triangle is $67.5$square meters and the length of the base is $9$meters.

The objective is to find the height of the triangle.

Step 2. Concept Used

The area of a triangle having base as $b$and height as$h$is given by the formula$A=\frac{1}{2}bh$.

Step 3. Find the height

In the formula $A=\frac{1}{2}bh$, substitute $67.5$for $A$and $9$for $b$and we get

role="math" $$\begin{gathered} 67.5=\frac{1}{2}\times 9\times h \\ 67.5=4.5h \end{gathered}$$

Now divide both sides by $4.5$.

$\begin{array}{rcl}\frac{67.5}{4.5}& =& \frac{4.5h}{4.5}\\ 15& =& h\end{array}$

So the height of the triangle is$15$ meters.