Question

(a) The area of a rectangular parking lot is 8428 m²

If the width of the parking lot is 86 m, what is its length?
Length of the parking lot: _ m

(b) The perimeter of a rectangular pool is 376 m.
If the length of the pool is 99 m, what is its width?
Width of the pool: _m

Answer 1

a) 98m , b) 89m

Explanation:

(a) Given,

• The area of a rectangular parking lot is 8428 m²
• width of the parking lot is 86 m

To Find : Length of the Parking lot

Length of a rectangle shape can be derived by the formula,

`l = (A)/(w)`

`l = (8428)/(86)`

`l = 98m`

Hence , the length of a rectangular parking lot is 98m

(b) Given ,

• The perimeter of a rectangular pool is 376 m
• length of the pool is 99 m

To Find : The width of the rectangular pool

We take the width as variable 'x'

Now we plug it into the perimeter of a rectangle equation

`376 = 2(99 + x)`

Using distributive property we,

`376 = 198 + 2x`

We now flip the equation

`2x + 198 = 376`

`2x = 376 - 198` ( Transposing into the right hand side)

`2x = 178`

`x = (178)/(2)`

`x = 89`
`m`

Hence , the width of the rectangular swimming pool is 89m

Answer 2

a) Length of the parking lot: 98 m

b) Width of the pool: 89 m

Explanation:

a) The formula for the area of a rectangle is
`A=lw`.

We need to evaluate the length. Lets solve for
`l.`

`A=lw`

Divide both sides of the equation by
`w`.

`(A)/(w) =l`

We are given

`A=8428\\w=86`

Lets evaluate
`l`.

`(8428)/(86)=l`

`l=98`

b) The formula for the perimeter of a rectangle is
`P=2l+2w`.

We need to evaluate the width. Lets solve for
`w`.

`P=2l+2w`

Subtract
`2l` from both sides of the equation.

`P-2l=2w`

Divide each term by 2.

`(P)/(2) -(2l)/(2) =(2w)/(2)`

Simplify.

`w=(P)/(2)-l`

We are given

`P=376\\l=99`

Lets evaluate
`w`.

`w=(376)/(2)-99`

`w=188-99`

`w=89`