MATH SOLVE

4 months ago

Q:
# The length of a rectangle is 8 feet more than the width. If the width is increased by 4 feet, and the length is decreased by 5 feet, the area remains the same. Find the dimensions of the original rectangle.

Accepted Solution

A:

Answer:Width = 12 feetLength = 20 feetStep-by-step explanation:The area of a rectangle is A = l*w. Here the length is 8 feet more than the width or 8 + w and the width is w. So the area is A = w(8+w) = 8w + w²If the dimensions are changed then the expressions will change. The width is increased by 4 feet. This means the width w becomes w + 4. The length is decreased by 5 feet. This means the length becomes 8 + w - 5 = 3 + w. So the area of the new triangle is A = (w+4)(3+w) = w² + 7w + 12.Since the areas are the same, set them equal to each other and solve for w.w² + 7w + 12 = 8w + w² Subtract w² from both sides.7w + 12 = 8w Subtract 7w from both sides.12 = wThe original width w is 12 feet. This means the original length which was 8 + w = 8 + 12 = 20 feet.