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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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User RicoZ
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2 Answers

4 votes

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!

User Ellyn
by
5.0k points
1 vote

ANSWER

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.

User Pranjal Sahu
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5.2k points