A builder set up a wooden frame in which to pour concrete for a foundation to a house. The length of the wooden frame is 24 feet. The width is 32 feet. The diagonal is 40 feet. Which best describes the foundation?
The foundation cannot be a rectangle: 24 + 32 not-equals 40.
The foundation cannot be a rectangle: (24 + 32) squared not-equals 40 squared.
The foundation cannot be a rectangle: StartRoot 24 squared + 23 squared EndRoot not-equals 40 squared.
The foundation may be a rectangle: 24 squared + 32 squared = 40 squared.
The foundation may be a rectangle: 24 squared + 32 squared = 40 squared.
Jeremy is trying to explain why a triangle with side lengths 35, 30, 60 is not a right triangle. His explanation is shown below.
Step 1: 35 squared + 30 squared question mark equals 60 squared
Step 2: (35 + 30) squared question mark equals 60 squared
Step 3: 65 squared question mark equals 60 squared
Step 4: 4,225 not-equals 3,600
Which best describes Jeremy’s explanation?
Jeremy’s explanation is accurate.
Jeremy’s explanation is inaccurate. He wrote the leg lengths in the incorrect order in step 1.
Jeremy’s explanation is inaccurate. He incorrectly combined terms in step 2.
Jeremy’s explanation is inaccurate. He multiplied incorrectly in step 4.
Jeremy’s explanation is inaccurate. He wrote the leg lengths in the incorrect order in step 1.
Which triangle side lengths form a right triangle? Choose all that apply.
5, 6, 7
6, 8, 14
8, 15, 17
10, 12, 15
15, 20, 25
16, 18, 20
The triangle side lengths that form a right triangle are:
5, 6, 7
8, 15, 17
10, 12, 15
15, 20, 25
The areas of the squares formed by the side lengths of the triangles are given for each triangle below. Which triangles are right triangles? Select the three correct answers. (Figures are not drawn to scale.)
3 squares form a triangle. The squares have areas 6 inches squared, 10 inches squared, 8 inches squared.
4 squares form a triangle. The squares have areas 9 inches squared, 25 inches squared, 16 inches squared.
5 squares form a triangle. The squares have areas 25 inches squared, 169 inches squared, 144 inches squared.
6 squares form a triangle. The squares have areas 7 inches squared, 25 inches squared, 24 inches squared.
7 squares form a triangle. The squares have areas 64 inches squared, 225 inches squared, 289 inches squared.
8 squares form a triangle. The squares have areas 10 inches squared, 26 inches squared, 24 inches squared.The areas of the squares formed by the side lengths of the triangles are given for each triangle below. Which triangles are right triangles? Select the three correct answers. (Figures are not drawn to scale.)
3 squares form a triangle. The squares have areas 6 inches squared, 10 inches squared, 8 inches squared.
4 squares form a triangle. The squares have areas 9 inches squared, 25 inches squared, 16 inches squared.
5 squares form a triangle. The squares have areas 25 inches squared, 169 inches squared, 144 inches squared.
6 squares form a triangle. The squares have areas 7 inches squared, 25 inches squared, 24 inches squared.
7 squares form a triangle. The squares have areas 64 inches squared, 225 inches squared, 289 inches squared.
8 squares form a triangle. The squares have areas 10 inches squared, 26 inches squared, 24 inches squared.
The triangles that are right triangles are:
3 squares form a triangle. The squares have areas 6 inches squared, 10 inches squared, 8 inches squared.
5 squares form a triangle. The squares have areas 25 inches squared, 169 inches squared, 144 inches squared.
8 squares form a triangle. The squares have areas 10 inches squared, 26 inches squared, 24 inches squared.