Question 171389: A rectangular swimming pool has length 30 m by 20 m. There is a deck of uniform width surrounding the pool. The area of the pool is the same as the area of the deck. Write a quadratic equation to model this situation and use it to determine the width of the deck.
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! A rectangular swimming pool has length 30 m by 20 m. There is a deck of uniform width surrounding the pool. The area of the pool is the same as the area of the deck. Write a quadratic equation to model this situation and use it to determine the width of the deck.
======================================
The area of the pool is 30m times 20m = 600m^2.
Let x = uniform width around the pool.
Width of bigger rectangle around the pool or deck = 2x + 20.
Length of bigger rectangle around the pool or deck = 2x + 30.
The question tells us that the area of the deck = the area of the pool.
We know the area of the pool = 600m^2.
So, your equation is:
(2x + 30) (2x + 20) = 600m^2
1.Solve for x.
2.Plug your value for x in the width of the bigger rectangle given above, which is the width of the deck.
Can you take it from here?
==========================
I received your reply.
The answer for x has to be positive.
I got two answers for x:
x = 5 and x = -30.
You did not use FOIL correctly. That is why your answers for x were 3-digit numbers.
Now, we totally reject x = -30 because distance is always positive.
For example. if you live 150 feet from the store, you would say:
I live 150 feet from the store.
You would not say: I live -150 feet from the store.
Now the width for the deck is: 2x + 20 and the length of the deck is
2x + 30.
To find the the right answers, replace x with 5 in BOTH expressions and you will find the right measurements for the deck of the pool.
Is this clear?
|
|
|
