RD Sharma Class 7 Solutions Chapter 15 - Properties of Triangles (Ex 15.5) Exercise 15.5 - Free PDF
FAQs on RD Sharma Class 7 Solutions Chapter 15 - Properties of Triangles (Ex 15.5) Exercise 15.5
1. How do the step-by-step RD Sharma Class 7 Maths Solutions for Exercise 15.5 help in mastering the Pythagoras theorem?
The RD Sharma solutions for Exercise 15.5 provide a detailed, methodical approach to solving problems based on the Pythagoras theorem. Each solution breaks down complex questions into simple, understandable steps. This helps students learn the correct method for identifying the hypotenuse, applying the formula a² + b² = c² correctly, and solving for unknown side lengths, which is crucial for building a strong foundation for exams.
2. What is the Pythagoras property of a triangle as explained in Chapter 15?
The Pythagoras property, or theorem, states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (legs). If 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse, the formula is a² + b² = c². This property is exclusively used for right-angled triangles.
3. How can I correctly identify the hypotenuse in any right-angled triangle?
Identifying the hypotenuse correctly is the most critical first step. There are two simple rules to remember:
The hypotenuse is always the side directly opposite the 90° angle.
It is always the longest side of the right-angled triangle.
Even if the triangle is rotated, finding the right angle first will immediately show you which side is the hypotenuse.
4. What is a common mistake students make when solving problems in RD Sharma Exercise 15.5?
A very common mistake is confusing the formula when trying to find one of the shorter sides (a leg) instead of the hypotenuse. Students sometimes incorrectly add the squares (e.g., a² = c² + b²) when they should be subtracting. The correct formula to find a leg 'a' is a² = c² - b². Always remember to subtract the square of the known leg from the square of the hypotenuse.
5. How is the angle sum property of a triangle related to solving problems in this exercise?
While Exercise 15.5 focuses on the Pythagoras theorem (side lengths), the angle sum property (all angles in a triangle sum to 180°) is also fundamental. In a right-angled triangle, one angle is always 90°. This means the other two acute angles must add up to 90°. This property helps in verifying if a triangle is a right-angled triangle or in solving more complex geometric problems where both angles and side lengths are involved.
6. What is a Pythagorean triplet and how do you verify if three numbers form one?
A Pythagorean triplet is a set of three positive integers, say a, b, and c, that perfectly satisfy the Pythagoras theorem, where a² + b² = c². To verify a triplet, you must:
Identify the largest number, which would be the hypotenuse 'c'.
Square the two smaller numbers and add their results.
Check if this sum is equal to the square of the largest number.
For example, for (6, 8, 10), we check if 6² + 8² = 10². This becomes 36 + 64 = 100, which is true. So, (6, 8, 10) is a Pythagorean triplet.
7. Can the Pythagoras theorem be used for any triangle?
No, the Pythagoras theorem is a special property that only applies to right-angled triangles. For acute or obtuse triangles, this relationship (a² + b² = c²) does not hold true. The presence of a 90° angle is essential for the theorem to be applicable. Using it on other types of triangles will lead to incorrect calculations of side lengths.
8. What types of questions can I expect in Exercise 15.5 on the Properties of Triangles?
The solutions for RD Sharma Exercise 15.5 cover a range of problem types designed to test your understanding of the Pythagoras theorem. You will typically find questions on:
Finding the length of the hypotenuse when the two legs are known.
Calculating the length of an unknown leg when the hypotenuse and the other leg are given.
Verifying if a given triangle is a right-angled triangle by checking if its sides form a Pythagorean triplet.
Solving word problems based on real-life scenarios, such as finding the height a ladder reaches on a wall or calculating distances.
