Question :- The perimeter of a rectangle is 240 cm. If its length is decreased by 10% and its breadth is increased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.
Solution :-
Given perimeter = 240,
i.e., 2(l + b) = 240
=> l + b = 120 cm.
Perimeter = 2(length + breadth)
Let length of the rectangle be x cm. Then, breadth of the rectangle = (120 – x) cm
The length is decreased by 10%,
10
So new length = x – x × --------
100
x
= x – ------------
10
10x – x
= -------------
10
9x
= ------------- cm.
10
Breadth is increased by 20%, so new breadth is
= (120 – x) + ( 120 – x) × 20/100
= (120 – x) + (120 – x) × 1/5
5 (120 – x) + ( 120 – x)
= ---------------------------------------
5
600 – 5x + 120 – x
= --------------------------------
5
720 – 6x
= ---------------------- cm
5
By the condition, perimeter remains the same,
i.e., 240 cm.
（ 9x 720 – 6x )
So, 2 × （ ---------- + ---------------- ) = 240
（ 10 5 )
9x 720 – 6x
⇒ ---------- + ---------------- = 240 / 2
10 5
9x + 2 (720 – 6x)
⇒ ---------------------------- = 120
10
⇒ 9x + 1440 – 12x = 120 × 10
⇒ -3x = 1200 – 1440
⇒ -3x = -240
⇒ x = -240 / -3
= 80
Length of the rectangle = x = 80 cm and
Breadth = 120 – x = 120 – 80 = 40 cm.
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