SOLUTION: The area of a rectangle is 54 cm². Its length and breadth are reduced by 5 cm and 2 cm, respectively, so as to become a square. Find the length of a side of the square.

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Question 1204196: The area of a rectangle is 54 cm². Its length and breadth are reduced by 5 cm and 2 cm, respectively, so as to become a square. Find
the length of a side of the square.
Found 2 solutions by math_tutor2020, Edwin McCravy:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

L = length
W = width
L*W = 54


L becomes L-5
W becomes W-2
At this point, we have a square
L-5 = W-2
L = W-2+5
L = W+3

L*W = 54
(W+3)*W = 54
W^2+3W = 54
W^2+3W-54 = 0
(W+9)(W-6) = 0
W+9 = 0 or W-6 = 0
W = -9 or W = 6
Ignore the negative value of W.
L = 54/W
L = 54/6
L = 9
The original rectangle is 9 cm by 6 cm.

9-5 = 4
6-2 = 4
The rectangle turns into a 4 cm by 4 cm square.


Answer: 4 cm
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Here's the picture. The large 9x6 rectangle has 54 little squares (square
centimeters of area) and the little 4x4 square outlined in red has 4x4 = 16
little squares (square centimeters of area). 

Notice that we took 5 cm off the length and 2 cm off the width (or height)
to have just that 4x4 square.



Edwin
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