Question

the perimeter of a rectangle is 240 metre if its length a decrease by 10% and breadth is increased by 20% we get the same perimeter find the length and the breadth of the both rectangles​

Answer 1

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