SOLUTION: the length and width of a rectangle are given by consecutive integers. the area of the rectangle is 90cm^2. find the length of a diangonal of the rectangle

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Question 141626: the length and width of a rectangle are given by consecutive integers. the area of the rectangle is 90cm^2. find the length of a diangonal of the rectangle
Found 2 solutions by checkley77, solver91311:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
x(x+1)=90
x^2+x-90=0
(x+10)(x-9)=0
x-9=0
x=9 answer for the shortest side
9+1=10 is the longer side.
proof
9*10=90
90=90

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
If the width is x, then the length must be x + 1 because the dimensions are consectutive integers. The given area is 90, so x%28x%2B1%29=90

x%28x%2B1%29=90

x%5E2%2Bx-90=0

Solve the quadratic excluding the extraneous negative root to get the width, add 1 to get the length, and then use the Pythagorean Theorem to calculate the length of the diagonal. You should probably leave your answer in terms of a radical, but if you do choose to express the numerical approximation, it should be rounded to the nearest centimeter. That's because your least precise given measurement -- the area -- was given to the nearest square centimeter.