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.
Algebra ->
Test
-> Lessons
-> 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.
Log On
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.
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.
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
(