The length of the rectangle is 4ft greater than the width. if each dimesion is increased by 3,the new area will be 33 square feet long. find the dimensions of the original rectangle

Width is 2 feet and the length is 6 feet.

Step-by-step explanation:

The area of a rectangle is A = l*w. Here the length is 4 feet more than the width or 4 + w and the width is w. So the area is A = w(4+w) = 4w + w²

If the dimensions are changed then the expressions will change. The width is increased by 3 feet. This means the width w becomes w + 3. The length is increased by 3 feet. This means the length becomes 4 + w + 3 = 7 + w. So the area of the new triangle is A = (w+3)(7+w) = w² + 10w + 21.

The new area is 33 feet longer. We can add 33 to the original area then set them equal to each other and solve for w.

w² + 10w + 21 = 33+4w + w²                Subtract w² from both sides.

10w + 21 = 33+4w                                 Subtract 4w from both sides.

6w + 21 = 33                                         Subtract 21 from both sides.

6w = 12                                                 Divide by 6.

w = 2 feet

The original width w is 2 feet. This means the original length which was 4 + w = 4 + 2 = 6 feet.

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