Question

the perimeter of a rectangle is 480 CM if its length is increased by 10% and and breadth is decreased by 20% we get the same perimeter find the length and breadth of the rectangle​

Answer 1

Step-by-step explanation:

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

Answer 2

Length of the rectangle = 80 cm

ngth of the rectangle = 80 cmand breadth of the rectangle = 160 cm

GIVEN :

The perimeter of a rectangle = 480 CM

If its length is increased by 10% and and breadth is decreased by 20% we get the same perimeter

TO FIND :

The length and breadth of the rectangle

SOLUTION :

Perimeter = 480 cm

And, perimeter of a rectangle = 2(length+breadth)

So, 2(L+B) = 480

or L + B = 480/2

or L = 240 - B -----(1)

Now, length of second rectangle = L + 10/100 L = L + L/10 = 11L/10

and breadth of second rectangle = B - 20/100 B = B - B/5 = 4B/5

So, 2(11L/10 + 4B/5) = 480

or (11L + 8B)/10 = 2400

=> 11L + 8B = 2400

=> 11 (240 -B) + 8B = 2400

=> 2640 - 11B + 8B = 2400

=> 2640-2400 = 11B - 8B

=> 240 = 3B

Hence, B = 240/3

or, B = 80cm

So, L = 240 - 80 = 160 cm

Therefore, length of the rectangle = 80 cm

length of the rectangle = 80 cmand breadth of the rectangle = 160 cm

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