# Word Problems Involving Width, Length, and Area

The formula for the area of a rectangle is

$A=w×h$

where $A$ is the area, $w$ is the width, and $h$ is the height.

The formula for the area of a triangle is

$A=\frac{1}{2}b×h$

where $A$ is the area, $b$ is the base and $h$ is the height.

You'll often encounter word problems where two of the values in one of these formulas are given, and you're required to find the third.

Example 1:

A rectangular city block is divided into $56$ square plots of equal size. If there are $14$ plots along the length of the block, how many plots are there along the width of the block?

This is an area problem where the "unit" is a square plot. The city block is a rectangle with area $56$ , and the length is $14$ . Substitute in the formula.

$56=w×14$

Divide both sides by $14$ .

$4=w$

So, the city block is $4$ plots wide.

Example 2:

Carlos is surveying a plot of land in the shape of a right triangle. The area of the land is $45,000$ square meters. If one leg of the triangular plot is $180$ meters long, what is the other leg of the triangle?

This is an area problem involving the formula for a triangle. Since it's a right triangle, one leg can be considered as the base, and the other as the height. Substitute $45000$ for $A$ and $180$ for $b$ in the formula.

$45000=\frac{1}{2}\left(180\right)h$

Simplify.

$45000=90h$

Divide both sides by $90$ .

$\frac{45000}{90}=h$

$500=h$

The other leg of the triangle is $500$ meters long.