The perimeter of a rectangle is 240cm. If it's length is decreased by 10% and breadth is increased by 20%, we get the same perimeter. Find the length and the breadth of the both the rectangles
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Answer:
Perimeter of the rectangle given = 240cm
Let x cm be the length of the rectangle,
Let y cm be the breadth of the rectangle,
According to the question:
2(x+y)=240
⇒x+y=120 [First equation]
Now, its length is increased by 10% and its breadth is decreased by 20%
So, the new length be= x+
100
10
x
=
100
100x+10x
=
100
110x
=
10
11x
And the new breadth be = y−
100
20
y
=
100
100y−20y
=
100
80y
=
10
8y
With new length and breadth we get same perimeter.
So,
⇒2(
10
11
x+
10
8
y)=240
⇒
10
11
x+
10
8
y=120
⇒11x+8y=1200 [Second equation]
Now, Second equation −8× [First equation], we get
3x=240
⇒x=80
Putting this value isn First equation,
y=120−80=40
So, length =x=80 cm
and Breadth=y=40 cm
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