What is the equation for the word problem

Question

Grant Wood painted his most famous painting, American Gothic in 1930 on composition board with perimeter 108.44 in. if the rectangular painting is 5.54 in. taller than it is wide, find the dimensions of the painting

Answer 1

First of all, as a refresher, here is the formula for finding perimeter:

 

2l + 2w = perimeter

 

We already know the perimeter, so we can plug that in --> 2l + 2w = 108.44in.

 

In regards to the problem's wording, we can conclude that "wideness" is for width and "tallness" (for 2D shapes) is for the length. Now, let's look at the variables. We don't know either dimension, but we do know that the length is 5.54in taller than it is wide. From this statement, we can replace 'l' with 'w + 5.54'.

 

Now that we only have one variable in our equation, it makes solving for the dimensions a whole lot easier! 

 

2(w + 5.54) + 2w = 108.44

2w + 11.08 + 2w = 108.44

4w = 97.36

w = 24.34in

 

Then, we can plug our 'w' into our other expression to find the length:

 

24.34 + 5.54 --> 29.88in.

 

Hope that helps! :)