Question

The length of a rectangle is 4 inches less than 4 times the width. If the perimeter is 72 inches, find the length and the width of the rectangle.

Answer 1

Answer:

Length is 28. Width is 8.

Step-by-step explanation:

The perimeter of a rectangle is given by the following formula:

$P=2l+2w$

We know that the length is 4 inches less than 4 times the width. Therefore:

$l=4w-4$

Substitute this for l. Let's also substitute 72 for P. Therefore:

$72=2(4w-4)+2w$

Distribute:

$72=8w-8+2w$

Combine like terms:

$72=10w-8$

Add 8 to both sides:

$80=10w$

Divide both sides by 10:

$w=8$

Therefore, the width is 8.

The length is 4 less than 4 times the width. Thus: "

$l=4(8)-4$

Multiply:

$l=32-4$

Subtract:

$l=28$

Therefore, the length is 28 and the width is 8.

And we're done!