Question

A rectangular garden plot 16 m by 24 m is to be bordered by a strip of uniform width x m wide on the out side so as to double the area. find x

Answer 1

Solution is in the attachment..

Answer 2

Answer:

The width of the strip x is 4

Step-by-step explanation:

Given,

The length of the garden (L) = 16 m

The breadth of the garden (B) = 24 m

The width of the strip taken is x

The area of the rectangular garden with a strip(A1) is twice the area of the rectangular garden without a strip(A2).

To find,

The value of x.

Calculation,

The length of the garden with a strip of width x is (l) = (16 + 2x)

The breadth of the garden with a strip of width x is (b) = (24 + 2x)

But 2A1 = A2

⇒2 (L × B) = 2 (l × b)

⇒ 16 × 24 × 2= (16 + 2x)(24 + 2x)

⇒ 16 × 24 = (8 × x)(12 + x)

⇒ x² + 20x + 96 = 192

⇒ x² + 20x - 96 = 0

⇒ x = 4 or x = -24

But width cannot be negative

x = 4

Therefore, the width of the strip x is 4

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