A rectangle has a perimeter of 48 inches. If twice the length decreased by three is equal to three times the width, then find the length and width.

Question

MONEY MIXTURES AND PERIMETER

Answer 1

Hi Ariel L

Length is 15 inches

Width is 9 inches

For a rectangle, the Perimeter = 2* the length + 2* the width

We can

Let P = perimeter

Let L = length

Let W = width

We are given a perimeter of 48 and that twice the length decreased by three is equal to three times the width.

P = 2L + 2W

2L - 3 = 3W

so 2L = 3W + 3

We can put everything in terms of W with a simple substitution

Substituting 3W + 3 for 2L in the formula for the perimeter we have

48 = 3W + 3 + 2W

Combine like terms

48 = 5W + 3

Subtract 3 from both sides of the equation

45 = 5W

Divid both sides by 5

9 = W

2L = 3W + 3

2L = 27 + 3

2L = 30

Divide both sides by 2

L = 15

Checking in the Perimeter Equation

P = 2L + 2W

48 = 2(15) + 2(9)

48 = 30 + 18

48 = 48

Hope this helps

Answer 2

W = Width

L = Length

Equation 1: 2(L+W) = 48 OR 2W + 2L = 48

Equation 2: 2L - 3 = 3W

Let's solve for one variable by plugging Equation 1 into Equation 2.

2W + 2L =48

-2L

2W = 48 - 2L

2W/2 = (48-2L)/2

W=24-L

Now that we know what W equals, when we plug it into Equations 2, we will only be solving for L.

2L - 3 = 3(24-L)

2L - 3 = 72 - 3L

*Let's get L on one side of the equation so we can solve for it*

2L - 3 = 72 -3L

+3L +3L

5L - 3 = 72

+3 +3

5L = 75

5L/5 = 75/5

L = 15

Now that we've solved for L, plug that number into equation 1 to find W

2W + 2(15) = 48

2W + 30 = 48

-30 - 30

2W = 18

W /2 = 18/2

W = 9

Lastly, to check your answers plug both variables into Equations 2.

2L - 3 = 3W

2(15) - 3 = 3(9)

30 - 3 = 27

27 = 27, TRUE, answers are correct.