SOLUTION: A rectangle, with a diagonal of length 10 inches,has length two inches longer than it's width.what is the length of the rectangle?

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Question 887175: A rectangle, with a diagonal of length 10 inches,has length two inches longer than it's width.what is the length of the rectangle?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle, with a diagonal of length variable c, 10 inches,has length two inches longer than it's width, L=w+2. what is the length of the rectangle?

Pythagorean Theorem will help.
highlight_green%28w%5E2%2B%28w%2B2%29%5E2=10%5E2%29, but you could rework the equation to use L and not w. But continuing,
w%5E2%2Bw%5E2%2B4w%2B4=100
2w%5E2%2B4w=96
w%5E2%2B2w=48
w%5E2%2B2w-48=0
%28w-6%29%28w%2B8%29=0
The meaningful answer for w is highlight%28w=6%29.
This will mean for L,
L=w%2B2
L=6%2B2
highlight%28L=8%29


This part was obviously wrong.....
cross%282w%5E2%2B4w%2B16-100=0%29----THIS was the mistake.
2w%5E2%2B4w-84=0
w%5E2%2B2w-42=0
Discriminant, cross%284-4%2A%28-42%29=4%2B4%2A42=172%29
172=43%2A4
-
w=%28-2%2Bsqrt%2843%2A4%29%29%2F2---Choosing the PLUS form, because the negative solution of w has no meaning for us here....
w=%28-2%2B2sqrt%2843%29%29%2F2
cross%28w=-1%2Bsqrt%2843%29%29.

The description gave L=w+2.
L=-1%2Bsqrt%2843%29%2B2
cross%28L=1%2Bsqrt%2843%29%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A rectangle, with a diagonal of length 10 inches,has length two inches longer than it's width.what is the length of the rectangle? 


Length of rectangle: highlight_green%28highlight_green%288%29%29 inches



You can do the check!! 



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