Question

gabriella wants to tile a room with an area of 320 square feet. the width of the room is 4/5 its length. what are the length and width of the room?

Answer 1

Assuming the shape of the room is a rectangle :

Area = Width x Length.

Let's call width "w" and length "l" . Now if, the width is 4/5 of the length that means 4/5 times length gives us the width, like this :

$w=\frac { 4 }{ 5 } \cdot l$

As given in the question, area of the rectangle is 320 square feet. And as I said before area of a rectangle can be found by multiplying its length and width. 

$w.l=320$

$w=\frac { 4 }{ 5 } \cdot l$ , we can plug w's value in the previous equation to find "l". 

$\frac { 4 }{ 5 } \cdot l\cdot l=320\\ \\ \frac { 4 }{ 5 } \cdot { l }^{ 2 }=320\\ \\ { l }^{ 2 }=320\cdot \frac { 5 }{ 4 } \\ \\ { l }^{ 2 }=\frac { 320\cdot 5 }{ 4 } \\ \\ { l }^{ 2 }=\frac { 1600 }{ 4 } \\ \\ { l }^{ 2 }=400\\ \\ \sqrt { { l }^{ 2 } } =\sqrt { 400 } \\ \\ l=20$

Let's plug "l"s value in the equation.

$w.l=320\quad \Longrightarrow \quad w\cdot 20=320\quad \Longrightarrow \quad w=\frac { 320 }{ 20 } \quad \Longrightarrow \quad w=16$

The length is 20 feet and the width is 16 feet.

Answer 2

Area equals to length times width
The length is 20 and the width is 16