SOLUTION: In the accompanying diagram the width of the inner rectangle is represented by x length by 2x-1. the width of the outer rectangle is represented by x+3 and the length by x+5. Qu

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Question 935128: In the accompanying diagram the width of the inner rectangle is represented by x length by 2x-1. the width of the outer rectangle is represented by x+3 and the length by x+5.
Questions
1. What's the outer region as a trinomial in terms of x?
2 If the perimeter of the outer rectangle is 24, what is the value of x?
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
If your listed dimensions correspond, then x%3Cx%2B3 and 2x-1%3Cx%2B5.
Those give 0%3C3 and x%3C6; Because x must be nonnegative, the description means
0%3Cx%3C6.

"Region" should mean "area". The area for the outer rectangle is %28x%2B3%29%28x%2B5%29=highlight%28x%5E2%2B8x%2B15%29.

Outer perimeter given as 24,
2%28x%2B3%29%2B2%28x%2B5%29=24
x%2B3%2Bx%2B5=12
2x%2B8=24
2x=16
highlight%28x=8%29
This disagrees with the description. Were the dimensions not described in corresponding parts?

The areas for the two rectangles could be examined in order to further see what restriction is needed
for x.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
x length by 2x-1.
the width of the outer rectangle is x+3 and the length x+5.

Area of outer region= Area of outer rectangle - area of inner rectangle
(x+3)(x+5) - x(2x-1)
x^2+8x+15 -2x^2-x
-x^2+7x+15
Area of outer region=-x^2+7x+15
Perimeter = 2(l+w)
= 2(x+3+x+5)
=2(2x+8)
4x+16 =24
4x=8
x=2