Question

A rectangle has a width of x centimetres and a perimeter of 8x centimetres. A square has

sides of length one fourth the length of the rectangle.
a) Determine the length of the rectangle.
b) Determine the perimeter of the square.
c) Determine how many centimetres greater the rectangle's perimeter is than the square's
perimeter if x = 4.
d) Determine how many square centimetres greater the rectangle's area is than the square's
area if x = 4.

Answer 1

Part A) The length of rectangle is
`3x`
`cm`

Part B) The perimeter of the square is
`3x`
`cm`

Part C)
`20`
`cm`

Part D)
`39`
`cm^2`

Explanation:

Part A) Find the length of the rectangle

we know that

The perimeter of rectangle is equal to

`P=2(L+W)`

we have

`P=8x`
`cm`

`W=x`
`cm`

substitute and solve for L

`8x=2(L+x)`

`4x=(L+x)`

`L=4x-x=3x`
`cm`

Part B) Find the perimeter of the square

we know that

The perimeter of a square is

`P=4b`

we have that

`b=(1/4)L`

substitute the value of L

`b=(1/4)3x=(3/4)x`
`cm`

Find the perimeter of the square

`P=4(3/4)x=3x`
`cm`

Part C) Find how many cm greater the rectangle's perimeter than the square's perimeter if x=4

Find the value of rectangle's perimeter

`P=8x`
`cm` ------>
`P=8(4)=32`
`cm`

Find the value of square's perimeter

`P=3x`
`cm` ------>
`P=3(4)=12`
`cm`

Find the difference

`32`
`cm`
`-12`
`cm`
`=20`
`cm`

Part D) Find how many square cm greater the rectangle's area is than the square's area if x=4

Find the value of rectangle's area

`A=(3x)(x)=3x^2`
`cm^2` ------>
`A=3(4^2)=48`
`cm^2`

Find the value of square's area

`A=((3/4)x)^2`
`cm^2` ------>
`A=((3/4)(4))^2 = 9`
`cm^2`

Find the difference

`48`
`cm^2`
`-9`
`cm^2`
`=39`
`cm^2`