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Answers
Answer:
Original Measurements: L = 80cm, B = 40cm
New Measurements: L = 72cm, B = 48cm
Step by step explanation:
Given that
Perimeter of rectangle = P= 240 cm
Suppose L is length and B is breadth of rectangle. So, as we know
Perimeter of Rectangle = 2(length + breadth)
P = 2(L + B)
240 =2(L + B)
L + B = 120 ....(1)
Now lets increase the breadth by 20 percent and decrease the length by 10 percent, and find the perimeter.
P = 2 (0.9L + 1.2B)
As the perimeter remains same, so
240 = 2(0.9L + 1.2B)
0.9L + 1.2B = 120 ..... (2)
Comparing equation (1) and (2)
L + B = 0.9L + 1.2B
L - 0.9L = 1.2B - B
0.1L = 0.2B
B = 0.1L ÷ 0.2
B = 0.5L .....(3)
Now substitute the value of B into equation (1)
L + 0.5L = 120
1.5L = 120
L = 120 ÷ 1.5
L = 80 cm
Now, substitute value of L into equation (3)
B = 0.5(80)
B = 40cm
So orignal rectangle had L = 80cm and B= 40cm
The length and breadth of new rectangles can be calculated as follows
L' = 0.9L
L' = 0.9(80)
L' = 72cm
B' = 1.2B
B' = 1.2(40)
B' = 48 cm