DER THINKING SKILLS
1. The perimeter of a rectangle is 240 cm. If its length in decreased by 10% and
breadth in increased by 20%, we get the same perimeter. Find the length
and breadth of the rectangle.
QUESTIONS find by one variable
Answers
❍ Let the Length be l cm and Breadth be b cm of the Rectangle.
¤ We're given with the perimeter of the rectangle, which is 240 cm. To find out the perimeter of the rectangle the formula is given by :
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⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀
⠀
- If the length of the rectangle is decreased by 10 % and the breadth of the rectangle is increased by 20 %, we get the same perimeter.
⠀
&
⠀
⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀
✇ Now, by putting the value of length and breadth in the above formula —
⠀
⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀
✇ We know the, value of Breadth, now putting value of 'b' in eqⁿ ( 1 ) to find the value of 'l' —
⠀
⠀
∴ Hence, Length and Breadth of the rectangle are 80 cm and 40 cm respectively.
Given :-
The perimeter of a rectangle is 240 cm. If its length in decreased by 10% and
breadth in increased by 20%, we get the same perimeter.
To Find :-
Length and breadth
Solution :-
Let the length be x and breadth be y
For length
Length decreased by 10%
x - 10% of x
x - 10/100 of x
x - 10/100 × x
x - 1/10 × x
x - x/10
10x - x/10
9x/10
For Breadth
Breadth increased by 20%
y + 20% of y
y + 20/100 of y
y + 20/100 × y
y + 2/10 × y
y + 2y/10
10y + 2y/10
12y/10
Given,
Perimeter is 240 cm
240 = 2(x + y)
240/2 = x + y
120 = x + y
120 - y = x (1)
240 = 2(9x/10 + 12y/10)
240/2 = (9x + 12y/10)
120 = 9x + 12y/10
120 × 10 = 9x + 12y
1200 = 9x + 12y
Divide both sides by 3
1200/3 = 9x + 12y/3
400 = 3x + 4y
400 = 3(120 - y) + 4y
400 = 360 - 3y + 4y
400 - 360 = -3y + 4y
40 cm = y
Now
For length
x + y = 120
x + 40 = 120
x = 120 - 40
x = 80 cm