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?(1 point)
To find the length of the side labeled with the question mark, we need to first find the area of the original rectangle before the rectangular area was removed.
The area of the original rectangle can be calculated as:
Area = length x width
Area = 3 feet x (2 feet + question mark)
Area = 3(2 + question mark)
We are told that the total area of the supply closet is 36 square feet. So, we can set up the following equation:
3(2 + question mark) - 8 = 36
6 + 3(question mark) - 8 = 36
3(question mark) = 38
question mark = 38 / 3
question mark ≈ 12.67 feet
Therefore, the length of the side labeled with the question mark is approximately 12.67 feet.
An illustration shows a triangle with a base labeled 8 inches. A line runs through the center of the triangle from the apex to the base. This perpendicular height is labeled 5 inches.
Crystal cuts a piece of wood into the shape of a triangle. The height of the triangle is 5 inches, and the base of the triangle measures 8 inches. Crystal makes a scale drawing of the triangle. If the height of her scale drawing is 2 inches, what is the area of her scale drawing?
(1 point)
Responses
6.4 square inches
6.4 square inches
3.2 square inches
3.2 square inches
20 square inches
20 square inches
1.6 square inches
1.6 square inches
To find the area of Crystal's scale drawing of the triangle, we can use the concept of similarity.
The ratio of corresponding sides in Crystal's scale drawing to the actual triangle is 2:5 (height) and 2:8 (base). This means that the scale factor is 2/5 to go from the actual triangle to the scale drawing.
To find the area of the scale drawing, we need to square this scale factor and then multiply it by the area of the actual triangle:
Scale factor = (2/5)^2 = 4/25
Area of the scale drawing = (4/25) x 1/2 x base x height
Area of the scale drawing = (4/25) x 1/2 x 8 x 2
Area of the scale drawing = (4/25) x 8
Area of the scale drawing = 32/25
Area of the scale drawing = 1.28 square inches
Therefore, the area of Crystal's scale drawing of the triangle is approximately 1.28 square inches.