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Linear Equations and Inequalities In one Variable | Linear Equations and Inequalities In one Variable Exercise 12.2

Question 26

A rectangle is 10 cm long and 8 cm wide. When each side of the rectangle is increased by x cm, its perimeter is doubled. Find the equation in x and hence find the area of the new rectangle.

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Given

Length of rectangle (l) = 10 cm and

Breadth of the rectangle = 8 cm

Perimeter = 2 (Length + Breadth)

= 2 (10 + 8) cm

= 2 × 18

= 36 cm

If each side of the rectangle is increased by x cm, then,

Perimeter = 2 (10 + x + 8 + x)

= 2 (18 + 2x)

= (36 + 4x) cm

According to the given condition,

36 + 4x = 2 (36)

36 + 4x = 72

4x = 72 – 36

4x = 36

x = 36 / 4

We get,

x = 9

Hence,

Length of new rectangle = 1 + x = 10 + 9 = 19 cm and

Breadth of new rectangle = b + x = 8 + 9 = 17 cm

Area = Length × Breadth = 19 × 17 cm2 = 323 cm2

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Question 26

A rectangle is 10 cm long and 8 cm wide. When each side of the rectangle is increased by x cm, its perimeter is doubled. Find the equation in x and hence find the area of the new rectangle.

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

Given

Length of rectangle (l) = 10 cm and

Breadth of the rectangle = 8 cm

Perimeter = 2 (Length + Breadth)

= 2 (10 + 8) cm

= 2 × 18

= 36 cm

If each side of the rectangle is increased by x cm, then,

Perimeter = 2 (10 + x + 8 + x)

= 2 (18 + 2x)

= (36 + 4x) cm

According to the given condition,

36 + 4x = 2 (36)

36 + 4x = 72

4x = 72 – 36

4x = 36

x = 36 / 4

We get,

x = 9

Hence,

Length of new rectangle = 1 + x = 10 + 9 = 19 cm and

Breadth of new rectangle = b + x = 8 + 9 = 17 cm

Area = Length × Breadth = 19 × 17 cm2 = 323 cm2

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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