Question

The length of a rectangle is 2 more than 3 times the width. If the perimeter is 100, find the length and width of the rectangle.

Answer 1

Answer:

The length is 38 units and the width is 12 units.

Step-by-step explanation:

We have to express the problem in equations.

$l$ is gonna be length, $w$ is gonna be width and $p$ is the perimeter.

The length is 2 more than 3 times the width is

$l=2+3w$

The perimeter is 100 refers to

$p=100$

Now, we know that the perimeter of a rectangle is expressed

$p=2(l+w)$

Replacing the first expression in the second equation, we have:

$100=2(2+3w+w)\\100=4+8w\\w=\frac{100-4}{8}=12$

Now, we replace this value in the first expression to find the length:

$l=2+3(12)=38$

Therefore, the length is 38 units and the width is 12 units.

Answer 2

L=17.49635531
W=5.715476066

100 = L X W
L = 2+ 3W 
Insert the L equation into the 1st equation, 2+ 3W x W = 100 
2+ 3W x W = 100
-2                    -2
3W X W = 98
3W^2 = 98
Divide both sides by 3
W^2 = 32.66
Square root both sides
now you have the Width, plug the width into the L X W = 100 equation, then divide 100 by the width, and now you have the length.