Question

Use the image to answer the question.

A composite shape is drawn, starting with a horizontally aligned rectangle. There is no measurement across the top, and the right side is labeled with a question mark. A horizontally aligned rectangular area marked as 8 feet in length and unknown in width is removed from the bottom left of the original rectangle. The remaining length on the right side is 2 feet. The remaining width on the left side is 3 feet. Corners are marked with right angles.

Tessa designs a supply closet as an addition to her house. The closet is pictured, and its total area is 36 square feet. What is the length in feet of the side of the supply closet labeled with the question mark?

Answer 1

Let the total height (the side with the question mark) be H and the height of the removed rectangle be h. The total width is 8 + 2 = 10 ft, and the leftover left-side height is 3 ft, so H = h + 3.

Area of the closet = area of full 10×H rectangle minus removed 8×h rectangle:
10H − 8h = 36.
Substitute h = H − 3: 10H − 8(H − 3) = 36 → 10H − 8H + 24 = 36 → 2H = 12 → H = 6.

Answer: 6 feet.