SOLUTION: A picture that is 18 inches by 12 inches has a frame of uniform width whose area is equal to that of the picture. Find the width o the frame.
You can put this solution on YOUR website! A picture that is 18 inches by 12 inches has a frame of uniform width whose area is equal to that of the picture.
Find the width of the frame.
:
find the area of the picture
18 * 12 = 216 sq/in
let x = the width of the frame
then the overall dimensions including the frame will be
(2x+18) by (2x+12)
:
Overall area - picture area = frame area
(2x+18)*(2x+12) - 216 = 216
FOIL
4x^2 + 24x + 36x + 216 - 216 = 216
A quadratic equation
4x^2 + 60x - 216 = 0
simplify divide by 4
x^2 + 15x - 54 = 0
Factors to
(x+18)(x-3) = 0
the positive solution is all we want here
x = 3 inches is the width of the frame
