If a rectangle has a P of 18 inches and another rectangle is formed by doubling the width and tripling the length, which has a perimeter of 46 inches, what is the L + W of the og triangle?

Question

Sorry, Im really confused with word problems.

i had to shorten to question so L=length / W=width / and og= original / in=inches

Answer 1

W - width of the original rectangle

L - length of the original rectangle

P_original - perimeter of the original rectangle

P_original = 18 (inches) ← given

P_original = 2W + 2L

2W + 2L = 18 → equation (1)

2W - width of the another rectangle

3L - length of the another rectangle

P_another - perimeter of the another rectangle

P_another = 46 (inches) ← given

P_another = 2W + 2W + 3L + 3L = 4W + 6L

4W + 6L = 46 → equation (2)

Solving the system of equations:

2W + 2L = 18 → equation (1) → multiply by "-2" and then add two equations

4W + 6L = 46 → equation (2)

-4W - 4L = -36

4W + 6L = 46

2L = 10 → solving for "L"

L = 5

Calculating "W" from equation (1):

2W + 2 • 5 = 18

W = 4

Answer 2

One key to word problems is to translate the English into math equation statements, usually sentence by sentence.

It is also frequently useful to write down any equations that you think might be applicable.

For instance, here the question involves "perimeter of a rectangle," so we might recall: P = 2L + 2W

We can use that to "translate" the first piece of info given: "a rectangle has a P of 18 inches" becomes

2L + 2W = 18

Then, "doubling the width and tripling the length" becomes New width = 2W and New length = 3L.

The new rectangle's perimeter is 2·3L + 2·2W = 46. So,

6L + 4W = 46

2L + 2W = 18. Multiply this 2nd eqn by -2:

-4L - 4W = - 36. Add this to the top eqn, left-hand side to left-hand side, right-hand side to right.

2L = 10 . You can probably take it from there ...