Grade 8 Pythagorean Theorem worksheet
from Gradelings · Name: ______________________
How to explain it
- It works for right triangles only.
- The two shorter sides (legs) are a and b. The longest side, across from the right angle, is c.
- a² + b² = c².
Example: A right triangle has legs 6 cm and 8 cm. How long is the longest side? 6² + 8² = 36 + 64 = 100. c = √100 = 10. Answer: 10 cm
Question 1
A right triangle has legs of 8 cm and 15 cm. How long is the hypotenuse?
answer boxcm
17 cm
Hint: c² = a² + b² = 64 + 225 = 289, so c = √289 = 17 cm.
Question 2
The hypotenuse of a right triangle is 10 cm and one leg is 6 cm. How long is the other leg?
answer boxcm
8 cm
Hint: b² = c² − a² = 100 − 36 = 64, so b = √64 = 8 cm.
Question 3
A triangle has sides 21 cm, 72 cm and 77 cm. Is it a right triangle?
- No
- Yes
No
Hint: Check whether 21² + 72² = 77²: 441 + 5184 = 5625, and 77² = 5929. They do not match.
Question 4
A ladder leans against a wall. Its foot is 40 m from the wall and it reaches 42 m up the wall. How long is the ladder?
answer boxm
58 m
Hint: The wall, ground and ladder make a right triangle. c² = 40² + 42² = 3364, so c = 58 m.
Question 5
A rectangular field is 20 m by 48 m. How long is the diagonal across the field?
answer boxm
52 m
Hint: The diagonal is the hypotenuse of a right triangle with legs 20 m and 48 m: √(400 + 2304) = √2704 = 52 m.
Question 6
The legs of a right triangle are 8 cm and 7 cm. What is the hypotenuse, rounded to 1 decimal place?
- 10.6 cm
- 15.0 cm
- 10.7 cm
- 3.9 cm
10.6 cm
Hint: c² = 8² + 7² = 113. √113 ≈ 10.6.
Question 7
The squares drawn on the two legs of a right triangle have areas of 196 cm² and 2304 cm². What is the area of the square on the hypotenuse?
answer boxcm²
2500 cm²
Hint: The Pythagorean theorem says the two smaller squares add up to the largest: 196 + 2304 = 2500 cm².
Question 8
In a right triangle, the hypotenuse is…
- any side next to the right angle
- the shortest side
- the longest side, opposite the right angle
- the side that is always 90°
the longest side, opposite the right angle
Hint: The hypotenuse faces the right angle, and it is always the longest side.
Question 9
A right triangle has legs of 3 cm and 4 cm. How long is the hypotenuse?
answer boxcm
5 cm
Hint: c² = a² + b² = 9 + 16 = 25, so c = √25 = 5 cm.
Question 10
The hypotenuse of a right triangle is 13 cm and one leg is 5 cm. How long is the other leg?
answer boxcm
12 cm
Hint: b² = c² − a² = 169 − 25 = 144, so b = √144 = 12 cm.
Answer key
- 1. 17 cm
- 2. 8 cm
- 3. No
- 4. 58 m
- 5. 52 m
- 6. 10.6 cm
- 7. 2500 cm²
- 8. the longest side, opposite the right angle
- 9. 5 cm
- 10. 12 cm
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