Question

A rectangular pool 12m x 8m is surrounded by a path of uniform width if area is 224 sq m find its width.

Answer 1

12 X 8 = 96 m^2

96 + 224 = 320 m^2

( 12 + 2x) ( 8 +2x) = 320

4x^2 +40x - 224 = 0

x^2 +10x - 56 = 0

( x+14) ( x-4) = 0

x = 4m ANSWER

Answer 2

Answer:

4 m

Step-by-step explanation:

Let the width of the path be x.

The outer length of the path = (12+ 2x)m

The outer breadth of the path = (8 + 2x)m

 

Area of the path = 224m2

ie, (12+2x)(8+2x) - (12)(8) = 224

⇒96 +24x + 16x + 4x2 - 96 = 224

⇒ 4x2 + 40x - 224 = 0

⇒ x2 + 10x - 56 = 0

⇒ x2 +14x - 4x - 56 = 0

⇒ x(x+14) - 4(x+14) = 0

⇒ (x-4)(x+14) = 0

x = 4 or x=-14

Since the width of a path cannot be negative we reject x=-14

Therefore, width of the path = 4m

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