# Thread: Can't find the dimension of this shape.

1. ## Can't find the dimension of this shape.

I'm in mathematic 112 (Pre-Algebra)

I'm supposed to find the dimensions of the fictional apartment in the picture (attached), with the given area of the whole apartement which is 450sq ft and area of the Living Room which is 180sq ft. I don't know where to start.

I have tried a lot of step but I keep getting it wrong.

I though I had to get the sum of all the areas of the home and set them equal to 450, but it's not working can you help me get started thanks.

2. ## Re: Can't find the dimension of this shape.

Originally Posted by mrjust
I'm in mathematic 112 (Pre-Algebra)

I'm supposed to find the dimensions of the fictional apartment in the picture (attached), with the given area of the whole apartement which is 450sq ft and area of the Living Room which is 180sq ft. I don't know where to start.

I have tried a lot of step but I keep getting it wrong.

I though I had to get the sum of all the areas of the home and set them equal to 450, but it's not working can you help me get started thanks.
let the left side of the apartment be (6+x) ft, and the bottom side be (y+10) ft.

we know

$$(6+x)(y+10) = 450$$

and

$$xy = 180$$

from the first equation

\begin{align*} \\ &6y + 10x + 60 + xy = 450 \\ &6y+10x + 60 + 180 = 450 \\ & 6y + 10x = 210\end{align*}

from the 2nd equation

\begin{align*} &x = 180/y \\ &6y + 10*180/y = 210 \\ &6y^2 - 210y + 1800 = 0 \\ &y^2 - 35y + 300 = 0 \\ &(y-15)(y-20) = 0 \\ &y = 15\mbox{ or }y = 20 \\ &x = 180/y\mbox{ so } \\ &(x,y) = (12,15)\mbox{ or }(9,20)\end{align*}

so there are two layouts that satisfy your requirements

1)
kitchen 6x15
living room 12x15 = 180
bedroom 10x18

total area is 18x25 = 450

2)
kitchen 6x20
living room 9x20 = 180
bedroom 10x15

total area is 15x30 = 450

3. ## Re: Can't find the dimension of this shape.

Thank you very much, it's very clear now. I appreciated very much! My mistake was using the same variable ( x ) for both the lenght and width.