Question

Topic - Linear Equations
Class - 8

The length of a rectangular field is 11 m more than its width. If the length is decreased by 12 m and the width is increased by 10 m, the area decreases by 24 m². Find the length and the width of the field.

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Answer 1

$\texttt{\textsf{\large{\underline{Solution}:}}}$

Let us assume that the breadth of the rectangle = x metre.

As length is 11 m more than breadth,

→ Length = x + 11 metre.

Area of the rectangle will be,

→ Area = Length × Breadth

→ Area = x(x + 11) m²

Now,

→ New length = (x + 11) - 12 metre = x - 1 metre.

→ New breadth = x + 10 metre.

Therefore,

→ Area = (x - 1)(x + 10) m²

According to question,

→ Area decreases by 24 m²

→ Original Area - New Area = 24 m²

→ x(x + 11) - (x - 1)(x + 10) = 24

→ x² + 11x - [x(x + 10) - 1(x + 10)] = 24

→ x² + 11x - [x² + 10x - x - 10] = 24

→ x² + 11x - [x² + 9x - 10] = 24

→ x² + 11x - x² - 9x + 10 = 24

→ 2x + 10 = 24

→ 2x = 14

→ x = 7 metre.

Therefore,

→ Breadth = x m = 7 m.

→ Length = x + 11 m = 18 m.

Which is our required answer.

$\texttt{\textsf{\large{\underline{Verification}:}}}$

Given,

→ Length = 18 m and Breadth = 7 m.

→ Original Area = LB = 7 × 18 m² = 126 m²

Now,

→ Length = 18 - 12 m = 6 m.

→ Breadth = 7 + 10 m = 17m.

→ New Area = 6 × 17 m² = 102 m²

So,

→ Original Area - New Area = (126 - 102) m²

= 24 m²

Hence Verified..!!