Pythagoras’ Theorem (Copy)
Q1 (Non-Calculator)
A right-angled triangle has sides 6 cm and 8 cm. Find the hypotenuse.
Solution:
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = √100
c = 10 cm
Answer:
10 cm
Q2 (Non-Calculator)
A right-angled triangle has a hypotenuse of 13 cm and one side of 5 cm. Find the other side.
Solution:
b² = 13² – 5²
b² = 169 – 25
b² = 144
b = √144
b = 12 cm
Answer:
12 cm
Q3 (Non-Calculator)
A triangle has sides of 7 cm and 24 cm. Find the hypotenuse.
Solution:
c² = 7² + 24²
c² = 49 + 576
c² = 625
c = √625
c = 25 cm
Answer:
25 cm
Q4 (Non-Calculator)
In a right-angled triangle, the hypotenuse is 17 cm and one side is 15 cm. Find the other side.
Solution:
b² = 17² – 15²
b² = 289 – 225
b² = 64
b = √64
b = 8 cm
Answer:
8 cm
Q5 (Non-Calculator)
Find the missing side of a right-angled triangle if one side is 9 cm and the hypotenuse is 12 cm.
Solution:
b² = 12² – 9²
b² = 144 – 81
b² = 63
b = √63
b ≈ 7.94 cm
Answer:
Approximately 7.94 cm
Q6 (Calculator)
A ladder is leaning against a wall. It reaches 5 m up the wall and the base is 3 m from the wall. Find the length of the ladder.
Solution:
c² = 5² + 3²
c² = 25 + 9
c² = 34
c = √34
c ≈ 5.83 m
Answer:
Approximately 5.83 m
Q7 (Calculator)
A ramp is 12 m long and rises vertically 5 m. Find the horizontal distance it covers.
Solution:
a² = 12² – 5²
a² = 144 – 25
a² = 119
a = √119
a ≈ 10.91 m
Answer:
Approximately 10.91 m
Q8 (Calculator)
In a right-angled triangle, sides are 9 m and 12 m. Find the hypotenuse.
Solution:
c² = 9² + 12²
c² = 81 + 144
c² = 225
c = √225
c = 15 m
Answer:
15 m
Q9 (Calculator)
A triangle has a hypotenuse 20 cm and one side 16 cm. Find the other side.
Solution:
b² = 20² – 16²
b² = 400 – 256
b² = 144
b = √144
b = 12 cm
Answer:
12 cm
Q10 (Calculator)
A rectangular field is 80 m long and 60 m wide. Find the diagonal across the field.
Solution:
c² = 80² + 60²
c² = 6400 + 3600
c² = 10,000
c = √10,000
c = 100 m
Answer:
100 m