What is the area of the painting with the frame? Without the frame? What happens if you subtract these two areas? Remember that the width of the frame is the same around the entire painting.
3 inches wide.
Practice makes perfect
Let's begin by plotting the painting with the frame. Let x be the width of the frame. Our mission is finding the value of x.
From this picture, we see that the area of the painting with the frame is given by the expression below.
A_(Total) = (24+2x)(16+2x)To find the area of just the frame, we subtract the area of the painting from the expression above.
A_(Frame) &= A_(Total) - A_(Painting)
&= (24+2x)(16+2x) - 24* 16
Let's simplify the right-hand side of the expression above.
Now, remember we are told that we have a total of 276in^2 to frame the painting.
A_(Frame) = 276 ⇒ 4x^2+80x = 276
By solving the equation above for x, we will find the width of the frame.
