Question

In a rectangle, the perimeter is 102 inches. The width of the rectangle is 9 inch more than half the length. What are the length and width of the rectangle?

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Answer 1

Hello!

The answer is: The length of the rectangle is 28 inches, while the width is 23 inches.

Why?

Perimeter is equal to the sum of all of the sides of the rectangle:

`P=2L+2W`

We know that the perimeter is 102 inches and width is 9 inch more than half of the length, so:

`Width=9+(1)/(2)*Length=9inches+0.5Length`

So, substituting the Width into the first equation, we have:

`102in=2L+2(9in+0.5L)\\\\102in=2L+18in+1L\\\\102in-18in=3L\\\\84in=3L\\\\L=(84in)/(3)=28`

Then, substituting L into the second equation, we have:

`Width=9inch+0.5(28inch)=9inch+14inch=23inch`

So, the length of the rectangle is 28 inches, while the width is 23 inches.

Have a nice day!

Answer 2

w=23 inches and l=28 inches.

Step-by-step explanation

The given rectangle has perimeter,

`p = 102in.`

The width of the rectangle is 9cm more than half the length.

`w = (1)/(2) l + 9`

Let the length be

`l`

inches.

The formula for perimeter is,

`p = 2l + 2w`

We substitute the values to get,

`102 = 2l + 2( (1)/(2)l + 9)`

Expand:

`102 = 2l + l + 18`

`102 - 18 = 3l`

`84 = 3l`

`l = 28in.`

The width is

`w = (1)/(2) (28) + 9`

`w = 14 + 9 = 23in.`