A rectangle has a width that is 1/8 its length. If the perimeter of the rectangle is 126 inches, what is the width of the rectangle?

Answer 1

l=8w
126=2l+2w
126=2l+2*1/8 l
126=2l+ l/4 l=2.25 l
solve for l, then w.

Answer 2

You were given:

A rectangle has a width that is 1/8 its length. If the perimeter of the rectangle is 126 inches, what is the width of the rectangle?

Length = we don't know and so I'll call it x.

Width = 1/8(x), which can be written x/8.

The perimeter given is 126 inches.

We use the formula for finding the perimeter of a rectangle.

P = 2L + 2W, where P = perimeter, L = length and W = width.

Is this clear so far?

126 inches = 2(x) + 2(x/8)

I will not use the word inches again for P because you know we are talking about a perimeter of 126 inches, right?

126 = 2x + x/4

We now have a fractional equation.

How do we remove the fraction part?

We multiply each term by the LCD, which so happens to be 4.

126(4) = 2x(4) + (x/4)(4)

504 = 8x + x

504 = 9x

To find x, we divide BOTH sides of the equation by 9.

504 divided by 9 = x

56 = x

We are looking for the width, right?

The width is (1/8)(x), which can also be written x/8.

We just found x, right?

To find the width, replace x with 56 in the fraction x/8 and then divide the numerator by the denominator.

So, x/8 becomes 56/8 = 7

What is the width of this rectangle?

Final answer: 7 inches.

That's it!