The Community Pool is going to add a sidewalk around the existing pool. Currently, the pool has a length of 32 feet and a width of 20 feet. The engineer designing the project knows that he has a total area of 1260 ft^2 for the existing pool and the sidewalk, but is unsure of how wide to design the sidewalk. a) Write an equation for the total area, A(x), where x represents the width of the sidewalk.

A.  38x 26 = 988

Step-by-step explanation:

The area of the pool with pathway = (32+2x)(20+2x) = 988 …. Eqn-1

[where x= width of the pathway]

The are of the pool alone = (32 x 20)= 640…… Eqn-2

So area of the pathway = 988- 640 = 248- feet

So [Eqn-1] -[Eqn-2] gives

So (32+2x)(20+2x)-640= 348

So 640+4x²+194x - 640= 348

So x²+26x-87= 0 I

So (x+29)(x-3)=0 So neglecting the negative value x= 3.

So the width of the side walk = 3- feet.

Check:

Length of the pool= 32+(3 x2)= 38′

Breadth of the pool= 20+(3x2)= 26′

Area of the SWIMMING POOL with sidewalk= 38x 26 = 988′

I hope this helps <3!

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