I can’t solve this.........

Question

A contractor is building a deck around a rectangular swimming pool. The deck is x feet from every side of the pool. Write an expression for the total area of the pool and deck, if the pool is 25 feet long and 20 feet wide. Find the area of the pool and deck.

Answer 1

Answer 2

Let's start this question by defining our variables; let's call the area of the pool A_p, the length of the pool L_p, the width of the pool W_p, the area of the deck A_d, the length of the deck L_d, and the width of the deck W_d. Let's also assume the variables are in feet, since that's what the problem gives.

Since the deck is built 5 feet from every side of the pool, we can say that the length of the pool, L_d, is equal to the length of the pool, L_p, plus 10. Don't forget that the 5 feet is built onto both sides of the pool, and thus 10 total feet is added to the length of the pool to find the length of the deck.

This comes out to L_d = L_p + 10.

We can do the same for the width of the deck, giving us the width of deck as: W_d = W_p + 10.

That just leaves us with the area. Since we've just defined the length and width of the deck, simply multiplying those numbers will gives us the area of both the deck and the pool, since the rectangle around the deck also encompasses the pool. Thus, we have to first multiply our deck length and width and then subtract the area of the pool in order to get the deck's area. This means:

A_d = L_dW_d - L_pW_p

But we can rewrite this entirely in terms of the pool's dimensions, like so:

A_d = (L_p+10)(W_p+10) - L_pW_p

And that's our expression! Now all we have to do is plug in the pool's dimensions to get the deck's area:

A_d = (25+10)(20+10) - (25)(20)

A_d = (35)(30) - (25)(20)

A_d = 1050 - 500 = 550

And voila! The area of the deck is 550 square feet.

You could also get this by splitting the deck's area into multiple rectangles around the pool, but just finding the total area of the deck and pool and then subtracting the pool is much easier (in my opinion).

Hopefully this helps! Feel free to follow up if it's still confusing or if you feel I did a poor job explaining.