Question

Need help with #4 (a,b,c). I’m in algebra 1 and this unit is Solving Systems by Substitution

Answer 1

4a)
`P=2L+2W`

4b)

`42=2L+2W\\L=2W+3`

4c)

`L=15\\W=6`

Explanation:

Note:

`P=` Perimeter

`L=` Length

`W=` Width

The perimeter of a rectangle is the sum of all its sides.

We can say

`P=L+L+W+W`

Which simplifies to

`P=2L+2W`

This is the equation to find the perimeter of a rectangle.

We are given the perimeter which is 42.

We are also given that the length is the sum of twice its width and 3.

So we can write

`42=2L+2W\\L=2W+3`

Lets solve using substitution.

Substitute
`L=2W+3` into the first equation.

`42=2W+2(2W+3)`

Expand the right side of the equation then simplify.

`42=2W+4W+6\\42=6W+6`

Subtract 6 from both sides.

`36=6W`

Divide both sides by 6 to isolate
`W`.

`W=6`

Perform a back substitution. Substitute
`W=6` into the second equation,
`L=2W+3`

`L=(2*6)+3\\L=12+3\\L=15`

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