The perimeter of a rectangle is 240 cm. If its length is decreased by 10% and breadth is increased by 20%, we get the same perimeter. Find the length and the breadth of the rectangle.
Answers
Step-by-step explanation:
UR QUESTION IS LITTLE BIT COMPLICATED .
HERE , WE GO ...
Perimeter of the given rectangle = 240cm
let the length of the the rectangle be = x cm
let the breadth of the rectangle be = y cm
A/Q
2( x + y ) =240
or x + y + 120 ------------(1) [ divided both sides by 2]
now,
let the new length be = x - 10/100 x [ since the length is decreased
by 10% ]
= (100x - 10x) 100 = 90/100x = 9/10x
let the new breadth be = y + 20/100y [ since the breadth is increased
by 20%]
= (100y = 20y)100 + 120/100y +12/10y
now, A/Q
2( 9/10x +12/10y) =240
or 9/10x + 12/10 = 120 ------------(2) [ divided both sides by 2]
from equation (1) and (2)
x+y = 9/10x + 12/10y
or 10(x +y) = 9x +12y [multiplied both sides by 10]
or 10x + 10y = 9x + 12y
or 10x - 9x = 12y - 10y
or x = 2y
or x - 2y = 0 --------------(3)
subtracting equation (3) from (1)
x + y - (x - 2y) = 120 - 0
or x + y -x + 2y = 120
or 3y = 120
or y = 120/3 = 40
so the breadth of the 1st rectangle is 40cm.
putting the value of y in equation (1) ---
x + y = 120
or x + 40 = 120
or x = 120 - 40 = 80
so the length of the 1st rectangle is 80cm.
now,
length of the 2nd rectangle = 9/10x = 9/10 x 80 = 72
breadth of te 2nd rectangle = 12/10y = 12/10 x 40 = 48
therefore, the length and breadth of the 1st rectangle is 80cm and 40cm respectively and the length and breadth of the 2nd rectangle is 72cm and 48cm respectively
HOPE , IT HELPS ... ✌
Step-by-step explanation:
SOLUTION
Given,
perimeter of rectangle = 240 cm
=> 2(Length + breadth) = 240cm
=> length + breadth = 120 cm
Find,
the length and the breadth of the rectangle.
Let the length of the rectangle be x cm
Then,
its breadth = (120 - x) cm.
Length is decreased by 10 %
Now,
new length = (1 - 10/100) × x cm
=> (1 - 1/10) x cm
=> 9/10x cm
Breadth is increased by 20%
new breadth = (1 + 20/100) × (120 - x) cm
=> (1 + 1/5) (120 - x) cm
=> 6(120 - x)/5 cm
According to given information, perimeter of the rectangle remains same
=> 2[9/10x + 6(120 - x)/5] = 240
=> 9/10x + 6(120 - x)/5 = 120
=> 9x + 12(120 - x) = 120 × 10
=> 9x + 1440 - 12x = 1200
=> -3x = 1200 - 1440
=> -3x = -240
=> x = -240/-3
=> x = 80