Question

The perimeter of a rectangle is 24 ft. Its length is five times its width Let x be the length and y be the width. What is the area of the rectangle?

Answer 1

`x=10" " y= 2" so area "=20 ft^2`

Explanation:

`color(brown)("Build the equation by breaking down the question into parts")`

Perimeter is `24 ft`

Width `->yft`
Length `"-> xft`

So perimeter is `->(2y+2x) ft=24 ft` ......................(1)

But Length = `5xx` width

So `x=5y` ..................................(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find y")`

Substitute equation (2) into equation (1) giving:

`2y+2(5y)=24`

`12y=24`

`color(brown)("y=2")` .....................................(3)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find x")`

Substitute (3) into (2) giving:

`color(brown)("x=5(2) -> x=10)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Check
`2x+2y = 24 " "=>" " 2(10)+2(2)=24 " "color(red)("True")`

Answer 2

`x=10,y=2`

`Area=20ft^2`

Explanation:

In the statement length is said to be `x` which is `5` times the width which is `y`

So,

`5x=y`

We can assume `y` as `x`

Then perimeter=`(5x+5x)+(x+x)=24`

`rarr10x+2x=24`

`rarr12x=24`

`rarrx=24/12=2`

So,the width=`2`

Then length=`2(5)=10`

Area of rectangle =`Leng` `th*width=10(2)=20ft^2`