SOLUTION: The perimeter of rectangular room is 32 m. The length of the diagonal is 8 m more than the width. Find the dimension of the room.

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Question 919246: The perimeter of rectangular room is 32 m. The length of the diagonal is 8 m more than the width. Find the dimension of the room.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w for width, L for length; and d for diagonal.
2w+2L=32 and d=8+w.

The diagonal serves as hypotenuse and w and L serve as legs of a right-triangle.
w^2+L^2=d^2.

Simplify the perimeter equation and substitute for d into the other two equations:
system%28w%2BL=16%2Cw%5E2%2BL%5E2=%28w%2B8%29%5E2%29;
Still needs a bit of simplification, and then just solve the system.


L=16-w;
Substitute...
w%5E2%2B%2816-w%29%5E2=w%5E2%2B16w%2B64
%2816-w%29%5E2=16w%2B64
16%5E2-32w%2Bw%5E2=16w%2B64
w%5E2-32w%2B16%5E2-16w-64=0
w%5E2-48w%2B16%5E2-64=0
highlight_green%28w%5E2-48w%2B192=0%29

w=%2848%2B-+sqrt%2848%5E2-4%2A192%29%29%2F2
w=%2848%2B-+8%2Asqrt%286%29%29%2F2
highlight%28w=24%2B-+4%2Asqrt%286%29%29, which are actually the two dimensions.