SOLUTION: The perimeter of a rectangle is 28 cm. if the length of a diagonal is 10 cm, find the length and width of the rectangle.
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Question 628163: The perimeter of a rectangle is 28 cm. if the length of a diagonal is 10 cm, find the length and width of the rectangle. Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! The perimeter of a rectangle is 28 cm. if the length of a diagonal is 10 cm, find the length and width of the rectangle.
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let x=length of rectangle
let y=width of rectangle
2x+2y=perimeter=28
x+y=14
y=14-x
by pythagorean theorem:
x^2+y^2=10^2=100
x^2+(14-x)^2=100
x^2+196-28x+x^2=100
2x^2-28x+196=100
2x^2-28x+96=0
x^2-14x+48=0
(x-8)(x-6)=0
x=8
or
x=6
length of rectangle: 8 cm
width of rectangle: 6 cm
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