Algebra Word Problem

Question

A picture has a square frame that is 2 in wide. The area of the picture is 1/3 the total area of the picture and frame. What are the dimensions of the picture?

 

We are working with the quadratic formula and I just need help to figure out how it works out into a formula! thanks!

Answer 1

 

I think you have to assume the picture is also a square?

Frame is thus 4 square inches.

Area of picture is X²= 1/3 (X²+4)

X²-1/3X²=4

2/3X²=4

X2=12/2=6

X is sq root of 6=2.5

Dimensions of picture are 2.5 by 2.5.

 

 

Answer 2

Let the picture have dimensions of x, and then the dimension of the picture and frame will be x + 4 (since there is a 2 inch wide frame all the way around. So, then the formula will be:

 

x^2= (1/3) (x+4)^2

 

When you work this out you will get a quadratic in x and can use the QE to solve.

 

- Ben