# Patio Dimensions

#### harpazo

##### Pure Mathematics
Banned
A contractor orders 8 cubic yards of premixed cement, all of which is to be used to pour a patio that will be 4 inches thick. If the length of the patio is specified to be twice the width, what will be the patio dimensions?

Note: 1 cubic yard = 27 cubic feet

Seeking the first-two steps.

#### MarkFL

##### La Villa Strangiato
Staff member
Moderator
Math Helper
The volume $$V$$ of the patio, in cubic feet, is:

$$\displaystyle V=w\ell\frac{1}{3}$$

We are told:

$$\displaystyle \ell=2w$$

Hence:

$$\displaystyle V=w(2w)\frac{1}{3}=\frac{2w^2}{3}$$

$$\displaystyle V=8\cdot27$$

Thus:

$$\displaystyle \frac{2w^2}{3}=8\cdot27$$

Solve for $$w$$.

• anemone and harpazo

#### harpazo

##### Pure Mathematics
Banned
The volume $$V$$ of the patio, in cubic feet, is:

$$\displaystyle V=w\ell\frac{1}{3}$$

We are told:

$$\displaystyle ell=2w$$

Hence:

$$\displaystyle V=w(2w)\frac{1}{3}=\frac{2w^2}{3}$$

$$\displaystyle V=8\cdot27$$

Thus:

$$\displaystyle \frac{2w^2}{3}=8\cdot27$$

Solve for $$w$$.
1. What is ell?

2. Where did 1/3 come from?

I understand why you multiplied 8 by 27.

#### MarkFL

##### La Villa Strangiato
Staff member
Moderator
Math Helper
1.) A typo, where I forgot to escape the string. Post corrected.

2.) 4 inches is 1/3 of a foot.

• anemone

#### harpazo

##### Pure Mathematics
Banned
1.) A typo, where I forgot to escape the string. Post corrected.

2.) 4 inches is 1/3 of a foot.
A foot = 12 inches

4/12 = 1/3

I see. I will continue when time allows.

#### harpazo

##### Pure Mathematics
Banned
The volume $$V$$ of the patio, in cubic feet, is:

$$\displaystyle V=w\ell\frac{1}{3}$$

We are told:

$$\displaystyle \ell=2w$$

Hence:

$$\displaystyle V=w(2w)\frac{1}{3}=\frac{2w^2}{3}$$

$$\displaystyle V=8\cdot27$$

Thus:

$$\displaystyle \frac{2w^2}{3}=8\cdot27$$

Solve for $$w$$. #### MarkFL

##### La Villa Strangiato
Staff member
Moderator
Math Helper
$$\displaystyle \frac{2w^2}{3}=8\cdot27$$

$$\displaystyle w^2=2^2\cdot3^4\implies w=2\cdot3^2=18\quad\checkmark$$

• harpazo and anemone

#### harpazo

##### Pure Mathematics
Banned
$$\displaystyle \frac{2w^2}{3}=8\cdot27$$

$$\displaystyle w^2=2^2\cdot3^4\implies w=2\cdot3^2=18\quad\checkmark$$
The width is 18 inches.

The length is twice the width or 36 inches.