SOLUTION: A picture 16 inches by 23 to be mounted on a piece of mat board so that there is an even amount of mat all around the picture. How wide will the border be if the area of the border

Algebra ->  Expressions-with-variables -> SOLUTION: A picture 16 inches by 23 to be mounted on a piece of mat board so that there is an even amount of mat all around the picture. How wide will the border be if the area of the border      Log On


   

Question 967416: A picture 16 inches by 23 to be mounted on a piece of mat board so that there is an even amount of mat all around the picture. How wide will the border be if the area of the border is 270 square inches?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
More general...
Picture dimensions x and y mounted on a mat board; uniform mat width w around the picture; mat border area is A.

You want to solve for w.
x, y, A, are known.

Total area minus picture area is the surrounding border area:
%28x%2B2w%29%28y%2B2w%29-xy=A, main starting equation.

xy%2B2yw%2B2xw%2B4w%5E2-xy=A
2yw%2B2xw%2B4w%5E2-A=0
yw%2Bxw%2B2w%5E2-A=0
2w%5E2%2B%28y%2Bx%29w-A=0
w=%28-%28x%2By%29%2B-+sqrt%28%28x%2By%29%5E2-4%2A2%2AA%29%29%2F%282%2A2%29, general solution of quadratic equation;
highlight%28w=%28-x-y%2B-+sqrt%28%28x%2By%29%5E2-8A%29%29%2F4%29

Substitute according to
x=16
y=23
A=270
and pick the positive result.