← Back to the Pythagorean Theorem worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 8.G.B.6, 8.G.B.7 · Level: Grade 8
Problem 1 Find the hypotenuse
20² + 21² = 400 + 441 = 841.
c = √841 = 29.
The hypotenuse is 29.
Problem 2 Find a leg
b² = 17² − 8² = 289 − 64 = 225.
b = √225 = 15.
The other leg is 15.
Problem 3 Irrational hypotenuse
c² = 6² + 7² = 36 + 49 = 85.
c = √85 ≈ 9.22.
The hypotenuse is about 9.2.
Problem 4 Leg to the nearest tenth
b² = 13² − 9² = 169 − 81 = 88.
b = √88 ≈ 9.38.
The leg is about 9.4.
Problem 5 Is it a right triangle?
The longest side is 41. 9² + 40² = 81 + 1,600 = 1,681, and 41² = 1,681.
The sums are equal, so the converse applies.
Yes, it is a right triangle
Problem 6 Read the figure
7² + 24² = 49 + 576 = 625.
√625 = 25.
Hypotenuse: 25
Problem 7 Not a right triangle
10² + 11² = 100 + 121 = 221, but 15² = 225.
The sums are not equal.
No, it is not a right triangle
Problem 8 Find x
x² = 34² − 16² = 1,156 − 256 = 900.
x = 30.
x = 30
Problem 9 Areas of squares
The square on the hypotenuse has area 25 + 144 = 169.
Its side is √169 = 13.
The hypotenuse is 13.
Problem 10 Short ladder
h² = 10² − 3.5² = 100 − 12.25 = 87.75.
h = √87.75 ≈ 9.37.
It reaches about 9.4 feet.
Problem 11 TV size
48² + 27² = 2,304 + 729 = 3,033.
√3,033 ≈ 55.07.
The diagonal is about 55 inches.
Problem 12 Right or not?
1.5² + 2² = 2.25 + 4 = 6.25, and 2.5² = 6.25.
Yes, it is a right triangle
Problem 13 Across the field
45² + 108² = 2,025 + 11,664 = 13,689.
√13,689 = 117.
The diagonal is 117 yards.
Problem 14 Isosceles right triangle
c² = 12² + 12² = 288, so c = √288 = 12√2.
12√2 ≈ 16.97.
12√2 cm ≈ 17.0 cm
Problem 15 Fire truck ladder
h² = 26² − 10² = 676 − 100 = 576.
h = 24.
The ladder reaches 24 feet.
Problem 16 Baseball throw
Home plate to second base is the diagonal of the square: d² = 60² + 60² = 7,200.
d = √7,200 ≈ 84.85.
The throw is about 84.9 feet.
Problem 17 Wheelchair ramp
Length² = 30² + 2.5² = 900 + 6.25 = 906.25.
Length = √906.25 ≈ 30.10.
The ramp is about 30.1 feet long.
Problem 18 Shipping box
d² = 12² + 16² + 21² = 144 + 256 + 441 = 841.
d = 29.
The longest rod is 29 inches.
Problem 19 Drone flight
Horizontal distance: √(36² + 15²) = √(1,296 + 225) = √1,521 = 39.
Straight-line distance: √(39² + 20²) = √(1,521 + 400) = √1,921 ≈ 43.83.
The drone is about 43.8 meters from the start.
Problem 20 Is the deck square?
2.4² + 3.2² = 5.76 + 10.24 = 16, so a right angle needs a diagonal of √16 = 4.
The measured 4.1² = 16.81, which does not equal 16.
No; the diagonal should be 4.0 meters