Question 978599: please help me to solve this.. the diagonal of a rectangle is 8 meters than its shorter side.if the area of the rectangle is 60 square meters,find its dimensions
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It helps to draw this.
I am assuming the diagonal is 8 meters longer than the shorter side.
There are now two sides of a right triangle.
The width is x
the length is y
xy=60
y=60/x
The two sides are legs of a right triangle, whose hypotenuse is the diagonal.
x^2+3600/x^2 = (x+8)^2=x^2+16x+64
3600/x^2=16x+64
divide by 16
225/x^2 =x+4
225= x^3+4x^2
x^3+4x^2-225=0
The roots are factors of 225. One can use synthetic division to find 5.
One can also graph this to show x=5
The sides are 5 and 12, the area 60, and the diagonal 13.
Alternative way on problems like this is to look at factors of 60, and see if one can make a right triangle with 5 for one leg, 12 for the other. When that is done, 13 becomes the answer.
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