# If the width of rectangle is 5 cm more than one-half of its length the perimeter is 70 cm, what are the dimensions of the rectangle?

Dec 4, 2016

The length is 20 cm and the width is 15 cm

#### Explanation:

First, let's call the width of our rectangle $w$ and the length $l$.

From the problem we know:

$w = \frac{1}{2} l + 5$

We also know the formula for the perimeter of a rectangle is:

$p = 2 \cdot l + 2 \cdot w$

So we can substitute $70$ for $p$ which is given in the problem and we can also substitute $\frac{1}{2} l + 5$ for $w$ and then solve for $l$:

$70 = 2 \cdot l + 2 \cdot \left(\frac{1}{2} l + 5\right)$

$70 = 2 l + 1 l + 10$

$70 = 3 l + 10$

$70 - 10 = 3 l + 10 - 10$

$60 = 3 l$

$\frac{60}{3} = \frac{3 l}{3}$

$20 = l$

Now we can substitute $20$ for $l$ in the formula for $w$ to find the width:

$w = \frac{1}{2} 20 + 5$

$w = 10 + 5$

$w = 15$