a painting is 3 inches longer than it is wide. it is set in a rectangular border that is 2 inches wider than the painting on each side. if the area of the border is 100in^2 what are the dimensions of the painting?
Here is a problem I worked for Jason that is almost the same. See if this won't do it.
http://www.jiskha.com/display.cgi?id=1164826659
To find the dimensions of the painting, we need to follow a step-by-step approach. Let's break down the problem:
1. Let's assume the width of the painting is "x" inches.
2. Since the painting is 3 inches longer than it is wide, the length of the painting would be "x + 3" inches.
3. The rectangular border is 2 inches wider than the painting on each side, so the width of the border is "(x + 2) + (x + 2)" inches.
4. The length of the border would be "(x + 3) + 2 + 2" inches.
5. To find the area of the border, we subtract the area of the painting from the area of the border.
Area of border = (length of border) * (width of border) - (length of painting) * (width of painting)
Given that the area of the border is 100in^2, we can write the equation:
100 = [(x + 3) + 2 + 2] * [(x + 2) + (x + 2)] - (x + 3) * x
Now, let's solve this equation to find the value of "x" (the width of the painting) and consequently determine the length of the painting:
1. Expand and simplify the equation:
100 = (x + 7) * (2x + 4) - x^2 - 3x
2. Distribute and simplify further:
100 = 2x^2 + 14x + 4x + 28 - x^2 - 3x
3. Combine like terms:
0 = x^2 + 15x + 28 - 100
4. Simplify:
0 = x^2 + 15x - 72
5. Factorize or use the quadratic formula to solve for "x."
Once you find the value of "x," substitute it back into the equation (x + 3) to find the length of the painting.
Using the solution from the link you provided, it should help you understand the step-by-step approach to solving this problem.