Question

9. The figure shows a rectangle with its length and breadth as indicated. Given that the perimeter of the rectangle is 120 cm, find the area of the rectangle. ​

Answer 1

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length and breadth as indicated:

3x - y

2x - 3

2x + y

2x - 3

3x - y + 2x - 3 + 2x + y + 2x - 3 = 120

3x + 2x + 2x + 2x - 3 - 3 = 120

9x - 6 = 120

9x = 120 + 6

9x = 126

$\sf \: x = \frac{126}{9}$

x = 14 = 3 × 14 - y = 42 - y

2x - 3 = 2 × 14 - 3 = 25

2x + y = 2 × 14 + y = 28 + y

2x - 3 = 25

=> 42 - y = 28 + y

=> 42 - 28 = y + y

=> 14 = 2y

=> y = 7

then 42 -y => 42 - 7 => 35

and 28 + y => 28 + 7 => 35

so the length is 35 and the width is 25

the area of the rectangle will be:

A = 35 × 25 = 875cm²

hope it was helpful to you

Answer 2

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length and breadth as indicated:

3x - y

2x - 3

2x + y

2x - 3

3x - y + 2x - 3 + 2x + y + 2x - 3 = 120

3x + 2x + 2x + 2x - 3 - 3 = 120

9x - 6 = 120

9x = 120 + 6

9x = 126

$\sf \: x = \frac{126}{9}$

x = 14 = 3 × 14 - y = 42 - y

2x - 3 = 2 × 14 - 3 = 25

2x + y = 2 × 14 + y = 28 + y

2x - 3 = 25

=> 42 - y = 28 + y

=> 42 - 28 = y + y

=> 14 = 2y

=> y = 7

then 42 -y => 42 - 7 => 35

and 28 + y => 28 + 7 => 35

so the length is 35 and the width is 25

the area of the rectangle will be:

A = 35 × 25 = 875cm²

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