Question

A rectangular pool 12 meters by 8 meters is surrounded by a walkway of width x meters. At what value of x will the area of the walkway equal the area of the pool?

Answer 1

Answer:

The width of the walkway is 2meter.

Step-by-step explanation:

Dimension of the rectangular pool is 12meter by 8 meter.

Area of the pool = 12×8=96 sq meter.

Now, let the width of the walkway be X.

Area of pool = (2×(12+2X) ×X) +(2×(8×X)) =96.

24X+4X^2+16X=96

4X^2+40X-96=0

X^2+10X-24=0

X^2+12X-2X-24=0

X(X+12) -2(X+12) =0

(X+12) (X-2) =0.

Either,

(X+12) =0

Or, X=-12 It is not possible.

Therefore,

(X-2) =0,

Or, X=2 It is the solution.