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

Question

asked Apr 28, 2023 173k views

1 Answer

Emobe · Answer 1 · 2023-05-04T13:24:23+0000

Answer:

4a)
P=2L+2W

4b)

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

4c)

$L=15\\W=6$

Explanation:

Note:

Perimeter

Length

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=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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