How to Solve Pythagorean Theorem Problems with Formula and Examples
In Maths, the Pythagorean theorem states that “In a right triangle, the square of the hypotenuse equals the sum of squares of the remaining two sides.”
Let’s solve some questions for further understanding -
Questions:
Identify the length of the hypotenuse in the given triangle -
Image - An Image of a Triangle
Identify the length of the perpendicular in the given triangle -
Image - An Image of a Triangle
Is the given figure a right-angled triangle?
Image - An Image of a Triangle
Identify the length of the base in the given triangle -
Image - an Image of a Triangle
Use Pythagoras' Theorem to check whether the given triangle is a right-angle triangle or not.
Image - an Image of a Triangle
Find the value of x.
Image - an Image of a Triangle
Pythagoras' theorem is applicable in which type of triangles?
[Acute triangles, right-angled triangles, or obtuse triangles]
Is the given triangle right-angled?
Image - an Image of a Triangle
Find the length of the hypotenuse in the given triangle.
Image - an Image of a Triangle
Find the length of the hypotenuse in the given triangle using Pythagoras' theorem.
Image - an image of a triangle
Does the Pythagorean theorem apply to right triangles?
Is the following Pythagorean triplet correct?
3, 4 and 5
Solve for an in the given triangle -
Image - an Image of a Triangle
Is the given figure a right-angled triangle?
Image - an Image of a Triangle
Solve for c in the given triangle -
Image - an Image of a Triangle
Answers -
8.1m, the hypotenuse length in the given triangle is 8.1m.
4cm 6cm, the perpendicular length in the given triangle can be 4cm or 6cm.
Yes, the given triangle is right-angled.
9cm or 12cm. The length of the base in the given triangle can be 9cm or 12cm.
By pythagoras theorem, a2+b2=c2
Let a=9 b=5 c=10.3
81 + 25 = 106 ⇔ 10.3 × 10.3 = 106 approx.
Therefore, LHS=RHS
Hence, the given triangle is a right-angle triangle.
By pythagoras theorem, a2+b2=c2
Given a=6 b=8
36 + 64 = c2 ⇒ 100 = c2
c = x = 10
Hence, the value of x is 10.
Pythagoras' theorem is applicable only in right-angled triangles.
No, the given triangle is not right-angled.
9.3cm the hypotenuse length in the given triangle is 9.3cm.
By Pythagoras' theorem, a2+b2=c2
Let a=3 b=7
9 + 49 = c2⇒ 58 = c2
c = √58
Hence, the hypotenuse length is √58.
Yes, the Pythagorean Theorem applies to all right-angled triangles.
By Pythagoras theorem, a2+b2=c2
Let a=3 b=4 c=5
9 + 16 =25
5 × 5 = 25
Therefore, LHS=RHS
Hence, 3, 4 and 5 are correct Pythagorean triplets.
Given, b=12 and c= 15
a2+b2=c2
a2+ 144 =225
Subtract 144 from each side to get:
144 - 144 + a2 = 225 - 144
a2 = 225 - 144 ⇒ a2 = 81
⇒ a = √81
a = 9
No, the given triangle is not right-angled.
Given, a=3 b=4
By Pythagoras’ theorem,
a2+b2=c2
32 + 42 = c2
3×3 + 4×4 =c2
9 + 16 = c2
25 = c2
c = √25
c = 5
Did You Know?
Were you aware that Pythagoras, the person who is credited for discovering the Pythagorean Theorem, claimed to have already lived four lives? Yes, the renowned mathematician claimed that he remembered the previous four lives that he had lived. Apart from that, he was also supposedly a great friend to animals and loved them very much.
Importance of Pythagorean Theorem Practice Questions for Students
Students of KG-3 will have to complete their Maths syllabus to gain a good understanding of the topics. In that process, the worksheets for the Pythagorean theorem can help them out. The concepts have been explained very well in the worksheets. Additionally, there are some very important questions hand-picked by the experts at Vedantu for a better student learning experience. They can score good marks on these worksheets.
The worksheets contain numerical problems, Pythagorean theorem word problems, real-time problems, and much more. By repeatedly solving the questions from the worksheets, students will gain a good understanding of the different topics and processes explained here. Students can rely on the authenticity of the worksheets as the questions are on par with the school board's standards. Students will also find the Pythagoras theorem chart depictions and learn how to create them.
Benefits of Pythagoras Theorem Practice Questions
Students can understand a lot about the topic by solving the questions from the worksheets.
Finding out the values related to the aspects of a right-angled triangle has been explained so that students can learn how to solve these questions.
The experts at Vedantu have provided an easy and simple explanation for all the solutions. Students will be able to understand the solutions without any additional effort easily.
Overall, the worksheets from Vedantu are resourceful study materials that will help the students prepare for their exams.
Students can rely on the authenticity of the worksheets and the solutions as they are entirely accurate and contain a lot of information that will be useful for students.
Download Pythagorean Theorem Worksheets From Vedantu
Your chance to download the Pythagorean triples examples with answers is right here. Get your hands on these helpful worksheets and better understand the concepts. These worksheets will help you practice appropriately so you can score some good marks in the examinations.
FAQs on Pythagorean Theorem Practice Questions and Worksheets
1. What is the Pythagorean Theorem?
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides, written as a² + b² = c². Here:
- a and b are the legs (shorter sides).
- c is the hypotenuse (longest side).
2. What is the formula for the Pythagorean Theorem?
The formula for the Pythagorean Theorem is a² + b² = c². In this formula:
- a = first leg
- b = second leg
- c = hypotenuse (side opposite the right angle)
3. How do you use the Pythagorean Theorem to find the hypotenuse?
To find the hypotenuse, substitute the legs into a² + b² = c² and solve for c. Steps:
- Square both legs.
- Add the squares.
- Take the square root of the sum.
- 3² + 4² = 9 + 16 = 25
- c = √25 = 5
4. How do you find a missing leg using the Pythagorean Theorem?
To find a missing leg, rearrange the formula to a² = c² − b² (or b² = c² − a²). Steps:
- Square the known sides.
- Subtract the smaller square from the hypotenuse square.
- Take the square root.
- 13² − 5² = 169 − 25 = 144
- a = √144 = 12
5. What is a Pythagorean triple?
A Pythagorean triple is a set of three whole numbers that satisfy a² + b² = c². Common examples include:
- 3, 4, 5
- 5, 12, 13
- 8, 15, 17
6. Does the Pythagorean Theorem only work for right triangles?
Yes, the Pythagorean Theorem only applies to right triangles. It works because one angle must be exactly 90°. For non-right triangles, other formulas like the Law of Cosines are used instead.
7. How can you tell if a triangle is a right triangle using the Pythagorean Theorem?
A triangle is a right triangle if its side lengths satisfy a² + b² = c². Steps:
- Identify the longest side as c.
- Square all three sides.
- Check if the two smaller squares add up to the largest square.
8. Can you give an example problem from a Pythagorean Theorem practice worksheet?
Yes, a common practice problem is: Find the missing side when a = 9 and b = 12. Solution:
- Use a² + b² = c²
- 9² + 12² = 81 + 144 = 225
- c = √225 = 15
9. What are common mistakes when using the Pythagorean Theorem?
Common mistakes when applying the Pythagorean Theorem include:
- Not identifying the hypotenuse correctly.
- Forgetting to take the square root at the end.
- Applying the formula to a non-right triangle.
- Making arithmetic errors when squaring numbers.
10. What are real-life applications of the Pythagorean Theorem?
The Pythagorean Theorem is used to calculate distances in construction, navigation, engineering, and coordinate geometry. Examples include:
- Finding the length of a ladder against a wall.
- Calculating the diagonal of a rectangle.
- Determining distance between two points using the distance formula, which is based on a² + b² = c².
