Use the image to answer the question.
A composite shape is drawn starting with a horizontally aligned rectangle with a length marked as a question mark along the top edge and a width of 7 centimeters marked along the left edge. A rectangular area is removed from the bottom right corner.
The removed area, of unknown length and width, leaves a remaining length of 4 centimeters along the bottom left of the original rectangle, and a remaining width of 4 centimeters along the upper right width of the original rectangle. Right angle marks are drawn in all 5 corners of the composite shape.
Sharona designs and builds this cover for a small six-sided box. Sharona knows that the area of the cover is 52 square centimeters. What is the length of the side of the figure labeled with a question mark? Express your answer in centimeters.
10
Since the total area of the composite shape is 52 square centimeters, and the original rectangle has an area of 7cm x ?cm = 7? square centimeters, we can find the area of the removed part by subtracting the area of the remaining rectangle (4cm x 4cm = 16 square centimeters) from the total area of the composite shape:
52 square centimeters - 16 square centimeters = 36 square centimeters
This 36 square centimeters is the area of the removed part, which is a rectangle with a length of ?cm and a width of ?cm.
To find the length of the side marked with a question mark, we can set up an equation:
(? x 7) - (4 x 4) = 36
7? - 16 = 36
7? = 52
? = 52 / 7
? = 10
Therefore, the length of the side of the figure labeled with a question mark is 10 centimeters.