PLS HELP algebra 2, linear systems

Question

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The length of a rectangle is 8.75 cm more than 3 times the width. If the perimeter of the rectangle is 89.5 cm, what are its demensions?

Answer 1

Hi Jordan,

For problems like this, setup is half the battle. First, assign your variables:

w=width of rectangle

L=3w + 8.75=length of rectangle--this is how you translate "8.75 more than three times the width"

Recall that the perimeter of a rectangle is given by:

P=2L + 2W

You were given:

P=89.5 cm.

So, go back and substitute into that equation:

89.5=2(3w+8.75) + 2w

Distribute:

89.5= 6w + 17.5 + 2w

Combine like terms:

89.5= 8w + 17.5

Subtract 17.5 on both sides to isolate w:

72=8w

w=9 cm.

Now that we know w, we can go back to the original equation we identified for length:

L=3W+8.75

L=3(9)+8.75

L=35.75 cm.

You can also check this by substituting 9 and 35.75 back into P=2L + 2W. You will come up with 89.5, which was indeed your perimeter.

Dimensions of the rectangle are 35.75 * 9 cm.

I hope this helps. The trick for these is appropriately assigning your variables. Good luck.

Answer 2

Let w be the width of the rectangle.

This makes the dimensions

(3w+8.75) × w.

Perimeter, P = 2Length+2width = 2(3w+8.75) + 2w = 89.5

8w+17.5 = 89.5

8w = 72

w = 9 cm

Length = 3w+8.75 = 27 + 8.75 = 35.75 cm

Dimensions:

Width = 9 cm

Length = 35.75 cm

Answer 3

You are given

L = 3W + 8.75

2L + 2W = 89.5

One way to solve this system of equations is to substitute L = 3W + 8.75, from the first equation, into the second equation. This gives

2(3W + 8.75) + 2W = 89.5

Now you can solve for W by the following steps:

6W + 17.5 + 2W = 89.5

8W + 17.5 = 89.5

8W = 89.5 - 17.5 = 72

W = 72/8 = 9

Now plug W = 9 into either of the first two equations and solve for L.

Hope this helps. Add a comment if you have any questions.