Answer :
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 :
[tex]w=\frac { 4 }{ 5 } \cdot l[/tex]
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.
[tex]w.l=320[/tex]
[tex]w=\frac { 4 }{ 5 } \cdot l[/tex] , we can plug w's value in the previous equation to find "l".
[tex]\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[/tex]
Let's plug "l"s value in the equation.
[tex]w.l=320\quad \Longrightarrow \quad w\cdot 20=320\quad \Longrightarrow \quad w=\frac { 320 }{ 20 } \quad \Longrightarrow \quad w=16[/tex]
The length is 20 feet and the width is 16 feet.
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 :
[tex]w=\frac { 4 }{ 5 } \cdot l[/tex]
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.
[tex]w.l=320[/tex]
[tex]w=\frac { 4 }{ 5 } \cdot l[/tex] , we can plug w's value in the previous equation to find "l".
[tex]\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[/tex]
Let's plug "l"s value in the equation.
[tex]w.l=320\quad \Longrightarrow \quad w\cdot 20=320\quad \Longrightarrow \quad w=\frac { 320 }{ 20 } \quad \Longrightarrow \quad w=16[/tex]
The length is 20 feet and the width is 16 feet.
area equals to length times width
The length is 20 and the width is 16
The length is 20 and the width is 16
