Problema Solution
The length of a painting is 2 inches longer than the width. The area of the painting is 48in^2. If a 3-inch frame is put around the painting, what is the area of the frame?
Answer provided by our tutors
Let
x = the width
x + 2 = the length
The area = width*length thus x(x + 2) = 48.
By solving the quadratic equation x(x + 2) = 48 we will find x:
x(x + 2) = 48
........
click here to see the quadratic equation solved for x
........
x = 6
We need to ignore the negative solution -8 since the width is always positive.
The total area of the painting together with the frame is: (x + 2*3)*(x + 2 + 2*3).
The area of the frame is:
(x + 2*3)*(x + 2 + 2*3) - x(x + 2) = 12x + 48
click here to see the step by step simplification of the above equation
Plug for x = 6:
12*6 + 48 = 120 in^2
The area of the frame is 120 in^2.