The perimeter of a rectangle is 240 cm.If it's length is decreased by

1.	The perimeter of a rectangle is 240 cm.If it's length is decreased by 10percent Nd breadth is increased by 20 percent,we get the same perimeter.find the original length and breadth of the rectangle.show the working.
Answer» Given, perimeter of RECTANGLE = 240 cm Let LENGTH of rectangle is L and breadth is B. perimeter of rectangle = 2(length + breadth) 240cm = 2(L + B) or, 120 = L + B L + B = 120 ..........(1) a/c to question, length is decreased by 10% . so, new length of rectangle = L - 10% of L = L - L/10 = 0.9L breadth of rectangle is increased by 20% so, new breadth of rectangle = B + 20% B = B + 20B/100 = 1.2B now, new perimeter of rectangle = 2(0.9L + 1.2B) but according to question, initial perimeter of rectangle = final perimeter of rectangle so, 240 = 2(0.9L + 1.2B) 0.9L + 1.2B = 120.........(2) from equations (1) and (2), MULTIPLYING 5 with equation (2) - 6 with equation (1) 5(0.9L + 1.2B) - 6(L + B) = 5 × 120 - 6 × 120 4.5 L - 6L = -120 -1.5L = -120 L = 80m and breadth = 120 - L = 40m HENCE, length of rectangle = 80m breadth of rectangle = 40m

The perimeter of a rectangle is 240 cm.If it's length is decreased by 10percent Nd breadth is increased by 20 percent,we get the same perimeter.find the original length and breadth of the rectangle.show the working.

Answer»

Given, perimeter of RECTANGLE = 240 cm

Let LENGTH of rectangle is L and breadth is B.

perimeter of rectangle = 2(length + breadth)

240cm = 2(L + B)

or, 120 = L + B

L + B = 120 ..........(1)

a/c to question,

length is decreased by 10% .

so, new length of rectangle = L - 10% of L

= L - L/10 = 0.9L

breadth of rectangle is increased by 20%

so, new breadth of rectangle = B + 20% B

= B + 20B/100 = 1.2B

now, new perimeter of rectangle = 2(0.9L + 1.2B)

but according to question,

initial perimeter of rectangle = final perimeter of rectangle

so, 240 = 2(0.9L + 1.2B)

0.9L + 1.2B = 120.........(2)

from equations (1) and (2),

MULTIPLYING 5 with equation (2) - 6 with equation (1)

5(0.9L + 1.2B) - 6(L + B) = 5 × 120 - 6 × 120

4.5 L - 6L = -120

-1.5L = -120

L = 80m and breadth = 120 - L = 40m

HENCE, length of rectangle = 80m

breadth of rectangle = 40m