SOLUTION: The length of a rectangle is 1cm longer than its width.
If the diagonal of the rectangle is 4cm, what are the dimensions of the rectangle?
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-> SOLUTION: The length of a rectangle is 1cm longer than its width.
If the diagonal of the rectangle is 4cm, what are the dimensions of the rectangle?
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Question 94036: The length of a rectangle is 1cm longer than its width.
If the diagonal of the rectangle is 4cm, what are the dimensions of the rectangle?
You can put this solution on YOUR website! width = w
length = w + 1
A diagonal of a rectangle makes a right triangle...
a = w
b = w + 1
c = 4
a^2 + b^2 = c^2
w^2 + (w + 1)^2 = 4^2
w^2 + w^2 + 2w + 1 = 16
2w^2 + 2w - 15 = 0
Use quadratic formula, or whatever you know how, to solve:
2w^2 + 2w = 15
w^2 + w = 15/2
(w + 1/2)^2 = 15/2 + 1/4 = 30/4 + 1/4 = 31/4
w + 1/2 = +- sqrt(31)/2
w = [ -1 +- sqrt(31) ]/2
The length is positive:
w = [ -1 + sqrt(31) ]/2
l = [ -1 + sqrt(31) ]/2 + 1 = [ -1 + sqrt(31) ]/2 + 2/2 = [ 1 + sqrt(31) ]/2
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