A rectangular pool 6 meters by 4 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?

The area of walkway equal to the area of poll for x = 0

Step-by-step explanation:

Given as:

The length of the rectangular pool = 6 m

The width of the rectangular pool = 4 m

So, The area of rectangular pool = Length * width

or, The area of rectangular pool = 6 m * 4 m = 24 m²

Now,

The pool is surrounded by walkway of x meter width

So, The new length = 6 + x + x = 6 + 2 x

And the new width = 4 + x + x = 4 + 2 x

So, The area of walkway = new length * new width

Or, The area of walkway = (6 + 2 x) * (4 + 2 x)

Or, The area of walkway = 24 + 12 x + 8 x + 4 x²

Or, The area of walkway = 4 x² + 20 x + 24

Now, ∵ The area of walkway = The area of pool

So, 4 x² + 20 x + 24 = 24

or, 4 x² + 20 x = 24 - 24

or, 4 x² + 20 x = 0

Or, 4 x (x + 5) = 0

Or, x = 0, x = - 5

So, At x = 0 both the area should be equal

Hence The area of walkway equal to the area of poll for x = 0 answer