SOLUTION: The perimeter of a rectangle is 30 cm and one of the diagonals is 5 root 5 cm. What are the length and width?

Question 340286: The perimeter of a rectangle is 30 cm and one of the diagonals is 5 root 5 cm. What are the length and width?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Perimeter P = 2*(L+W)=30
L+W= 15.
..
the side and the diagonal form a right triangle
L^2+W^2=(5sqrt5)^2
L^2+W^2=125
....
L+W=15
square both sides
(L+W)^2 = 225
L^+2LW+W^2= 225
L^2+W^2=125
2LW+125=225
2LW= 225-125
2LW= 100
LW= 50
W= 50/L
plug value of W in L+W=15
L+50/L = 15
L^2+50 /L = 15
L^2+50 = 15L
L^2-15L+50 =0
L^2-10L-5L+50 =0
L(L-10)-5(L-10)=0
(L-10)(L-5)=0
L= 10cm OR 5 cm
....
CHECK
10+10+5+5 = 30 the perimeter
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