The area of a rectangle is 35 feet^2, and the length of the rectangle is 8 feet less than three times the width. Find the dimensions of the rectangle

A = 35 ft^2 (square feet)

L=3W-8 (feet)

The formula for the area of this rect. is now A = W (3W-8) = 35 ft^2

3W^2 - 8W - 35 = 0

There are various ways in which we could solve this equation for W.

I have chosen to "factor by grouping."

3W^2 - 8W - 35 = 0

3W^2 - 15W + 7W - 35 = 0

3W (W-5) + 7 (W-5) = 0

Then (3W+7) (W-5) = 0, and W=-7/3 or W=5. Since W denotes width, and width cannot be negative, omit W=-7/3. Thus, W=width=5 feet.

Next, L=3W-8=3 (5) - 8=15-8=7 feet.

Check: Does (5 feet) (7 feet) come out to 35 square feet? YES.

The dimensions of this rectangle are 5 by 7 feet.