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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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kudzordzifrancis

ANSWER

w=23 inches and l=28 inches.

EXPLANATION

The given rectangle has perimeter,

[tex]p = 102in.[/tex]

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

[tex]w = \frac{1}{2} l + 9[/tex]

Let the length be

[tex]l[/tex]

inches.

The formula for perimeter is,

[tex]p = 2l + 2w[/tex]

We substitute the values to get,

[tex]102 = 2l + 2( \frac{1}{2}l + 9)[/tex]

Expand:

[tex]102 = 2l + l + 18[/tex]

[tex]102 - 18 = 3l[/tex]

[tex]84 = 3l[/tex]

[tex]l = 28in.[/tex]

The width is

[tex]w = \frac{1}{2} (28) + 9[/tex]

[tex]w = 14 + 9 = 23in.[/tex]

mixter17

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:

[tex]P=2L+2W[/tex]

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

[tex]Width=9+\frac{1}{2}*Length=9inches+0.5Length[/tex]

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

[tex]102in=2L+2(9in+0.5L)\\\\102in=2L+18in+1L\\\\102in-18in=3L\\\\84in=3L\\\\L=\frac{84in}{3}=28[/tex]

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

[tex]Width=9inch+0.5(28inch)=9inch+14inch=23inch[/tex]

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

Have a nice day!

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