Question

11. A rectangle's length is 5 cm less than twice
its width. If the length is decreased by 5 cm
and width is increased by 2 cm; the perimeter
of the resulting rectangle will be 74 cm. Find
the length and the width of the original
rectangle​

Answer 1

Answer:

Length=25cm

Width=15cm

Step-by-step explanation:

Let width of the original rectangle = x cm

Length of the original rectangle = (2x – 5)cm

Now, new length of the rectangle = 2x – 5 – 5 = (2x – 10) cm

New width of the rectangle = (x + 2) cm

New perimeter = 2[Length+Width] = 2[2x – 10 + x + 2] = 2[3x – 8] = (6x – 16) cm

Given; new perimeter = 74 cm

6x – 16 = 74

=> 6x = 74 + 16

=> 6x = 90

=>x = 15

Length of the original rectangle = 2x – 5 = 2 x 15 – 5 = 30 – 5 = 25 cm

Width of the original rectangle = x = 15 cm

Answer 2

let s take,

length = x

breadth = x

length is 5cm less than twice it's width

breadth = x

length = 2x - 5

if the length is decreased by 5cm and width is increased by 2cm

length = 2x - 5 - 5 = 2x + 10

breadth = x + 2

perimeter of rectangle = 74 cm

2 ( l + b ) = 74

2 ( 2x + 10 + x + 2 ) = 74

2 ( 3x + 12 ) = 74

6x + 24 = 74

6x = 74 - 24

6x = 60

x = 60 / 6

x = 10

length = 2x + 10 = 2(10) + 10 = 20 + 10 = 30

breadth = x + 2 = 10 + 2 = 12

Hence,

length = 30cm

breadth = 12cm

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