Thread: "Building a patio" problem, must write an equation

Here's a problem a friend and I have been trying to figure out. Maybe one of you will be able to help us?

Here it goes:

"Someone is planning to build a patio along the back wall of her house which is 32 feet long. The patio will be rectangular in shape and will fit against the full length of the back wall (so one side of the patio will be 32 feet long).

Let's assume the patio tiles are each 1ft x 1ft.

If this person has 256 tiles to work with, how far out from the wall will the patio extend?

Pretend you are the patio builder and do these tasks:

* Choose the variable you are going to use and state what it represents.

* Write an equation that represents the problem.

* Then solve the problem and equation.

Also ...

Benito is also going to build a patio but his patio does not have to fit exactly against a wall. In fact all that Benito has decided is that the patio should be rectangular in shape and should use all of the 144 tiles he has available. His tiles are the same size as the problem above.

Find as many possibilities you can for the dimensions of Benito's patio."

Any tips, suggestions, etc on how to solve this two are appreciated.

Ok, let's assume the following variables!

L= (The distance of the back wall = the length of the patio) = 32 feet (this is told to us)
W = how far the patio extends from the wall (what we're trying to find)
A = The total area of the patio tiles

Clearly, if the patio tiles are 1ft by 1ft big and there's 256 of these, then the total area (A) will be 256 feet squared, correct?

(1 patio tile = 1ft squared. Hence, 256 = 256 ft squared)
Therefore, A = 256 feet squared.


By using the Area formula for a rectangle (which happens to contain all of our variables) we can solve the problem:

A=L*W
256 = 32 * W

Solving for W:
256/32 = W

Therefore, W (what we're trying to find) = 8 feet

Hello Sarah-

Originally Posted by Sarah-

...

Benito is also going to build a patio but his patio does not have to fit exactly against a wall. In fact all that Benito has decided is that the patio should be rectangular in shape and should use all of the 144 tiles he has available. His tiles are the same size as the problem above.

Find as many possibilities you can for the dimensions of Benito's patio."

Any tips, suggestions, etc on how to solve this two are appreciated.

When you're building a rectangular patio, you can work out the number of tiles you'll need by multiplying the length of the patio by its breadth. For example, if the length is 10 feet and the breadth 6 feet, then the area of the patio is 10 x 6 = 60 square feet. So if each tile is 1 ft by 1 ft, that will use 60 tiles.

So, if you have 144 of these tiles, you can make any shape rectangle you like provided its length multiplied by its breadth is 144. I'll start you off:

1 ft x 144 ft (Well, it's possible, but it's a very long thin patio!)

2 ft x 72 ft

3 ft x 48 ft

... and so on. Can you find all the other possible shapes now? (Bear in mind that each number you choose will have to divide exactly into 144. So it's no good trying to make a patio measuring 5 feet along one side, is it?)

Grandad

I think so.... wouldn't the only other possible combination be 4 * 36? If not, please correct me.

Most certainly not,

This is just a matter of being proficient with your times tables. You're looking for two factors of 144 that are both whole integers (that is, not fractions nor decimals).

There are quite a number of combinations!

6 * 24
8 * 18
12 * 12
16 * 9

Can you think of anymore?