The longest side of a right-angled triangle is the hypotenuse, and sides 3, 4 and 5 make a right-angled triangle, so this Year 8 sheet opens by naming the longest side and testing the famous triple. The answers record 10 cm and 12 cm as missing sides.
Key Takeaways
The longest side of a right-angled triangle is the hypotenuse (Q1).
A triangle with sides 3, 4 and 5 is right-angled (Q2).
Q5 records 12 cm as a missing-side answer.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.In a right-angled triangle, the longest side is called the...
(a) base(b) hypotenuse(c) perpendicular(d) height
2.A triangle with sides 3, 4 and 5 is...
(a) not a right-angled triangle(b) a right-angled triangle(c) an impossible triangle(d) an equilateral triangle
3.In a right-angled triangle, the two shorter sides are 6 cm and 8 cm. What is the length of the hypotenuse?
(a) 10 cm(b) 14 cm(c) 12 cm(d) 100 cm
4.For a right-angled triangle with sides a and b and hypotenuse c, which statement is true?
(a) c² = a² + b²(b) c² = a² - b²(c) a = b + c(d) c = a + b
5.The hypotenuse of a right-angled triangle is 13 cm and one leg is 5 cm. What is the length of the other leg?
(a) 8 cm(b) 12 cm(c) 10 cm(d) 18 cm
6.Both shorter sides of a right-angled triangle are 1 cm. What is the length of the hypotenuse?
(a) 2 cm(b) √2 cm(c) √3 cm(d) 1 cm
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.State Pythagoras' theorem for a right-angled triangle with sides a and b and hypotenuse c.
8.Find the hypotenuse of a right-angled triangle with legs 5 cm and 12 cm.
9.In a right-angled triangle the hypotenuse is 10 cm and one leg is 6 cm. Find the length of the other leg.
10.Is a triangle with sides 6 cm, 8 cm and 10 cm a right-angled triangle? Show your working.
11.Find the hypotenuse of a right-angled triangle with legs 9 cm and 12 cm.
12.The legs of a right-angled triangle are 7 cm and 24 cm. Find the length of the hypotenuse.
13.Find the length of the diagonal of a rectangle that is 6 cm by 8 cm.
14.The hypotenuse of a right-angled triangle is 17 cm and one leg is 15 cm. Find the length of the other leg.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A ladder 5 m long leans against a wall. The foot of the ladder is 3 m from the bottom of the wall. How high up the wall does the ladder reach?
16.A right-angled triangle has legs of 8 cm and 15 cm. Find the length of its hypotenuse and the perimeter of the triangle.
17.A rectangle is 12 cm long and 9 cm wide. Find the length of its diagonal.
18.A square has sides of 4 cm. Find the length of its diagonal, leaving your answer in surd form.
19.A ship sails 6 km north and then 8 km east. How far is the ship from its starting point?
20.A triangle has sides 9 cm, 12 cm and 15 cm. Show that it is a right-angled triangle, then find its area.
Answer Key
1. b) hypotenuse
2. b) a right-angled triangle
3. a) 10 cm
4. a) c² = a² + b²
5. b) 12 cm
6. b) √2 cm
7. Refer to solution guide.
8. Refer to solution guide.
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18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the longest side of a right-angled triangle called?
The hypotenuse, option (b) in this worksheet (Q1).
Is a triangle with sides 3, 4 and 5 right-angled?
Yes, option (b) in this worksheet (Q2).
What is the length of a missing side in a 6, 8, c triangle?
10 cm, option (a) in this worksheet (Q3).
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