Question 464769
The perimeter of a rectangle is 34cm, and the diagonal is 13cm. Determine the lengths of the sides of the rectangle.
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let x=length of rectangle
let y=width of rectangle
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2x+2y=perimeter=34
divide by 2
x+y=17
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x^2+y^2=13^2=169  (Pythagorean Theorem)
y^2=169-x^2
y=ħsqrt(169-x^2)
since y>0, use the positive sqrt
x+y=17
x+sqrt(169-x^2)=17
sqrt(169-x^2)=17-x
square both sides
169-x^2=289-34x+x^2
2x^2-34x+120=0
x^2-17x+60=0
(x-5)(x-12)=0
x=5
y=17-x=12
or 
x=12
y=17-x=5
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ans:
length of rectangle=5
Width of rectangle=12 
or
length of rectangle=12
Width of rectangle=5