Length of the hypotenuse | Maths | Quizalize & Oak National Academy

Starter quiz

Which of these sides is a hypotenuse?
- side A
- side B ✓
- side C
- none of them are hypotenuses
- it is impossible to tell
The triangle formed from these three squares is right-angled. What is the value of $n$ , where $n$ units² is the area of a square.
- 2
- 4.9
- 12
- 24 ✓
- 290
If three squares with different areas are joined at their vertices, what type of triangle would be formed?
- acute triangle
- scalene triangle ✓
- isosceles triangle
- equilateral triangle
Angle $a°$ is an acute angle, but is the largest angle in this triangle. Which of these are possible values of $t$ , where $t$ units² is the area of a square.
- 17
- 19 ✓
- 20 ✓
- 32
- 34
Which of these are true for the Pythagoras' theorem?
- Describes a property of only equilateral triangles.
- Describes a property of only right-angled triangles. ✓
- Describes a relationship between the squares of the side lengths of a triangle. ✓
- Describes a relationship between the interior angles of a triangle.
- Describes a relationship between squares formed from the sides of a triangle. ✓
A right-angled triangle is formed from three squares. The area of two of the squares are 75 units² and 25 units². What are the possible areas of the third square?
- 3 units²
- 25 units²
- 50 units² ✓
- 100 units² ✓
- 6250 units²

Exit quiz

The length of the hypotenuse for this right-angled triangle is ______ cm.
- '11 cm' ✓
$k$ cm² is the area of the square from the hypotenuse of the triangle. The value of $k$ is ______.
- '67.24' ✓
Calculate the length of the hypotenuse of this triangle, in units.
- 10 units
- 12.69 units
- 14.14 units
- 19 units ✓
- 361 units
The area, $w$ , of the largest square in this diagram is ______ cm².
- '2664' ✓
Calculate the length of the hypotenuse for this triangle. (Give your answer to 1 d.p.).
- 24.1 units² ✓
- 506.8 units²
- 583 units²
- 256 889 units²
The length of the hypotenuse of this triangle, rounded to 1 d.p. is ______ cm.
- '23.4' ✓

Worksheet

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Lesson Details

Key learning points

The sum of the squares of the two shorter sides equals the square of the longest side.
The longest side is always opposite the right angle.
A calculator can perform these calculations efficiently.
Priority of operations makes the order clear.

Common misconception

Pythagorean triples can be a trio of any rational numbers that, when constructed into a triangle, always produces a right-angled triangle.

Pythagorean triples are conventionally a trio of integer side lengths of a right-angled triangle, such as the 3, 4, 5 triangle. Other, similar triangles can be generated from Pythagorean triples, whose side lengths are rational, such as 0.3, 0.4, 0.5

Keywords

Pythagoras’ theorem - Pythagoras’ theorem shows that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of its longest side (the hypotenuse).
Hypotenuse - A hypotenuse is the side of the right-angle triangle which is opposite the right-angle.
Right-angled triangle - A right-angled triangle has exactly one 90° interior angle.