SOLUTION: a rectangle has a perimeter of 36cm. the square of the length of its diagonal is 164 square metres. find the dimensions of the rectangle.

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Question 729830: a rectangle has a perimeter of 36cm. the square of the length of its diagonal is 164 square metres. find the dimensions of the rectangle.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter
2(l+w)=36
l+w=18

l^2+w^2= 164
(l+w)^2-2lw=164
18^2-2lw=164
324-21w=164
21w=160
lw=80
l=80/w
substitute l
in l+w=18
80/w + w = 18
multiply by w
80+w^2=18w
w^2-18w+80=0
(w-10)(w-8)=0
w=8 OR 10
so dimensions are 10cm & 8 cm