i need help with algebra word question

Question

a rectangles length is 8 cm more than 3 times its width. if the perimeter is 128 cm . what is the length and the width.

Answer 1

Todd, the key is to translate the sentences into equations.

Let's define L=Length of the rectangle and W=Width of the rectangle

 

The word "is" tells you where the equals sign is.

 

Your first sentence translates:

(a rectangles length) [is] 8 cm more than 3 times its {width}.

L = 8cm more than 3 times W

 

"times" usually means multiplication and "more than" usually means to add, so

L = 8cm more than 3 times W

L = 8 + 3xW or L=8+3W, which is the first equation.

 

The second sentence is

if the perimeter is 128 cm

The perimeter is the distance around the figure and for a rectangle, starting in the lower left corner, you go up the width (+1W), across the length to the right (+1L), down the width (+1W) and then back left across the length (+1L) or 1W+1L+1W+1L=2W+2L

 

So the second equation is the perimeter = 2W+2L=128

 

L=8+3W

2W+2L=128

 

With these two equations and two unknowns (L & W), there is a unique solution, which I leave for you.  I hope this helps.