Question

The perimeter of a rectangular swimming pool is 414 meters. The length of the pool is 7 meters more than four times the width. Find the length and the width.

Answer 1

Answer: Length= 167 meters, Width= 40 meters

Step-by-step explanation:

We know that perimeter is the lengths of all sides of the rectangle added together. Therefore, the formula for perimeter is $P=2l+2w$. We can use system of equations to find length and width.

$P=2l+2w$

$l=7+4w$

The second equation comes from the fact that the length is 7 meters more than 4 times the width.

Since we know the equation of $l$, we can use substitution to find $l$ and $w$.

$P=2(7+4w)+2w$

$P=14+8w+2w$

$P=14+10w$

The problem gives us the perimeter to we can plug that into P.

$414=14+10w$

$400=10w$

$w=40$

Now that we know the width, we can plug it into the equation to find length.

$l=7+4(40)$

$l=7+160$$l=167$