Pythagorean Theorem Quiz
Questions: 16 · 10 minutes
1. A ramp rises 3 feet vertically over a horizontal distance of 4 feet. How long is the sloping surface of the ramp?
1 foot, the difference between the rise and run
7 feet, the sum of the rise and run
5 feet, the hypotenuse of the right-triangle cross-section
The square root of 7 feet, from adding the rise and run before taking a root
2. A student adds leg lengths of 5 and 12 and claims that the hypotenuse is 17. What length should the student obtain by applying the Pythagorean theorem?
17 units, found by adding the two legs
The square root of 17 units, found from the sum of the legs
7 units, found by subtracting the shorter leg
13 units, found from the sum of the squared legs
3. In a right triangle, how is the hypotenuse identified?
It is the shortest side of the triangle.
It is the side opposite the right angle.
It is either side that forms the right angle.
It is the side opposite the smallest angle.
4. A triangle has side lengths 8, 15, and 17. Between which two sides is its right angle?
The sides of lengths 8 and 15
The sides of lengths 8 and 17
The sides of lengths 15 and 17
Every pair of sides forms a right angle.
5. A right triangle has legs measuring 6 units and 8 units. How long is its hypotenuse?
7 units
10 units
14 units
The square root of 28 units
6. A square has sides of length 7 units. What is the exact length of one diagonal?
7 units
14 units
The square root of 14 units
7 times the square root of 2 units
7. One leg of a right triangle is 8 units, and the hypotenuse is 17 units. What is the other leg's length?
25 units
15 units
12 units
The square root of 353 units
8. A triangle has side lengths 5, 6, and 8. Using the square comparison with 8 as the longest side, how is the triangle classified?
Obtuse, because 5 squared plus 6 squared is less than 8 squared
Acute, because 5 squared plus 6 squared is greater than 8 squared
It cannot form a triangle because the two shorter sides are insufficient.
Right, because 5 squared plus 6 squared equals 8 squared
9. An isosceles right triangle has a hypotenuse of 10 units. What is the exact length of each equal leg?
5 times the square root of 2 units
10 times the square root of 2 units
5 units
The square root of 10 units
10. Which statement gives the Pythagorean theorem when a and b are the legs of a right triangle and c is the hypotenuse?
The square of a minus the square of b equals the square of c.
The sum of a and b equals c.
The square of a plus the square of b equals the square of c.
Twice a plus twice b equals c.
11. A rectangular screen is 9 inches high and 12 inches wide. What is its diagonal length?
15 inches
13 inches
18 inches
21 inches
12. A right triangle has a hypotenuse of 13 units and one leg of 5 units. What is the length of the other leg?
8 units
The square root of 194 units
18 units
12 units
13. What is the distance between the points (1, 2) and (7, 10) on a coordinate plane?
100 units
14 units
The square root of 28 units
10 units
14. A 10-foot ladder rests against a wall, with its base 6 feet from the wall. Assuming the wall and ground meet at a right angle, how high does the ladder reach?
4 feet
8 feet
The square root of 136 feet
16 feet
15. A right triangle has legs of length 4 units and 5 units. What is the exact length of its hypotenuse?
9 units
The square root of 21 units
The square root of 41 units
41 units
16. Do side lengths 7, 24, and 25 form a right triangle?
No, because 7 plus 24 does not equal 25.
No, because the square of 25 exceeds each smaller square.
Yes, because 7 squared plus 24 squared equals 25 squared.
Yes, because 7 plus 24 is greater than 25.