A rectangle has a P of 18 in. A new rectangle is formed by doubling the W and tripling the L, and has a P of 46 in. What is the L and W of the og triangle?

Question

P= perimeter

W= width

L= length

Sorry I had to shorten some stuff because the question wouldnt fit.

I am doing a worksheet and I’m confused.

Answer 1

Perimeter of a rectangle is 2l + 2w, where l = length and w = width

From information we can create two equations in two unknowns:

2l + 2w = 18

6l + 4w = 46

multiply first equation by 2

4l + 4w= 36

6l + 4w = 46

subtract 2nd equation from 1st:

-2l = -10

l = 5

substitute value of l into first equation to solve for w:

2l + 2w = 18

2(5) + 2w = 18

10+ 2w = 18

2w = 8

w = 4

original rectangle is 5 x 4.

Answer 2

We can use the two equations

2L + 2W = 18

2(3L) + 2(2W) = 46

to solve for L and W. We can multiply the first equation by 2 and subtract the two sides from the second equation:

6L + 4W = 46

– 4L + 4W = 36

¯¯¯¯¯¯¯¯¯¯¯¯¯

2L = 10

L = 5

Then we can use L = 5 to solve for W in the first equation:

10 + 2W = 18

2W = 8

W = 4