Pythagoras questions with answers

Welcome to our Pythagoras' Theorem Questions area.

This gives us \[ ?^2 + 5^2 = 8^2 \]

So \[ ?^2 = 8^2 - 5^2 = 64 - 25 = 39 \]

This gives us \[ ?

Verify if it is a right-angled triangle.
A) Yes
B) No
Answer: A) Yes
Explanation: Check with the Pythagorean theorem: 10² + 24² = 100 + 576 = 676, and 26² = 676, so it is a right-angled triangle.

Question 9:
The hypotenuse of a right-angled triangle is 13 cm, and one leg is 5 cm.

Other formulas that can be deduced from the Pythagorean theorem

As a result of the formula \[ a^2 + b^2 = c^2 \] we can also deduce that:

• \[ b^2 = c^2 - a^2 \]
• \[ a^2 = c^2 - b^2 \]
• \[ c = \sqrt{a^2 + b^2} \]
• \[ b = \sqrt {c^2 - a^2} \]
• \[ a = \sqrt {c^2 - b^2} \]

Example 1) Find the length of the missing side.

In this example, we need to find the hypotenuse (longest side of a right triangle).

To do this, label the sides a, b and c (with c being the hypotenuse – the longest side). If you have a right angled triangle and you know two of the lengths, label the sides of the triangle a,b and c (c must be the hypotenuse – the longest side).

Pythagorean Theorem is a^2+b^2=c^2.

If Pythagoras' theorem is true for the triangle, and c² = a² + b² then the triangle is a right triangle.

If Pythagoras' theorem is false for the triangle, and c² = a² + b² then the triangle is not a right triangle.

A range of different measurement units have been used in the triangles, which are not drawn to scale.

The following questions involve using Pythagoras' theorem to solve a range of word problems involving 'real-life' type questions.

On the first sheet, only the hypotenuse needs to be found, given the measurements of the other sides.

Illustrations have been provided to support students solving these word problems.

Here you will find a support page packed with a range of geometric formula.

Here you will find help, support and questions to help you master Pythagoras' Theorem and apply it. Its simplicity and universality make it a fundamental concept in mathematics education worldwide.

The quickest way to assess the pythagorean theorem knowledge of candidates is using an AI assessment platform like OnlineExamMaker.

Learning how to use the Pythagorean Theorem to solve problems involving right triangles is a skill that every math student can learn with some consistent practice.

Here you will find a range of geometry cheat sheets to help you answer a range of geometry questions.

The sheets contain information about angles, types and properties of 2d and 3d shapes, and also common formulas associated with 2d and 3d shapes.

What is the length of the other leg?
A) 8 cm
B) 7 cm
C) 9 cm
D) 6 cm
Answer: A) 8 cm
Explanation: Using the Pythagorean theorem, b = √(c² – a²) = √(10² – 6²) = √(100 – 36) = √64 = 8 cm.

Question 4:
The sides of a right-angled triangle are 5 cm, 12 cm, and x cm, where x is the hypotenuse.

If a math problem is related to a triangle that does not have a 90-degree angle, then you likely can not use the Pythagorean Theorem to solve it.

However, in the case of all right triangles with the following properties:

• The legs of the right triangle (the two smaller sides) are a and b

• The hypotenuse of the right triangle (the longest side) is c

Then the following is always true: a² + b² = c²

In other words, the square of the length of the longest side, c, is equal to the sum of the squares of the two smaller sides, a and b.

To help you to visualize how the Pythagorean Theorem relates to a right triangle with side lengths a, b, and c (where c is the hypotenuse), take a look at Figure 01 below.

For example, let’s say that you have a triangle with side lengths 3, 4, and 5, and you wanted to confirm whether or not the triangle in question was a right triangle.

To verify whether or not the triangle is right, we would have to substitute the three side lengths into the Pythagorean Theorem, a² + b² = c², and see if the equation holds true.

And one of the best ways to consistently practice using the Pythagorean Theorem to solve right triangle problems is by working on a Pythagorean Theorem Worksheet or two assess your understanding and to keep your skills sharp!

If you are looking for effective Pythagorean Theorem Worksheets (that include both triangle diagram problems and word problems), then you’re in the right place!