Algebra Word Problem

Question

the perimeter of a pool table is 30ft. The table is twice as long as it is wide. What is the length of the pool table?

Answer 1

The perimeter of a rectangle can be expressed in two ways. You know that rectangles have two pairs of equal sides. (Each side is the same as the opposite side. All four sides, however, are not equal, or it would be a square). In math, we represent the sides' values as "Length" and "width". Since perimeter is the sum of all the sides together, we are left with:

 

P = L + w + L + w                            or                          P = 2L + 2w

 

 

"The table is twice as long as it is wide." This information allows you to adjust the unknown length (L) so that it can be expressed as "2w", since it tells you that the length is 2 times the width. (You could also represent the width as 0.5L and reach the same answer, but if you're already having trouble, I'd recommend avoiding decimals) Now you can restate your formula with all known variables:

 

P = 2L + 2w           -->          30 ft = 2(2w) + 2w           -->            30 ft = 4w + 2w           

 

You can add numbers with the same variables, so we get

 

30 ft = 6w

 

Divide both sides by 6 to get

 

5 ft = w

 

Always practice careful reading when it comes to math problems! Remember that the problem asks for the length of the pool table, not the width. However, you can now easily refer back to the statement "the table is twice as long as it is wide" to find the length!