# NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5

NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5 (Ex. 6.5) Triangles and its Properties free to use online or download to use it offline in PDF file format. All the contents are modified and updated for academic session 2021-2022 CBSE and state board.

Class 7 math exercise 6.5 is based on Pythagoras Theorem and angle sum properties of triangle. Some questions of this exercise are little bit tricky, so do it carefully.## Class 7 Maths Chapter 6 Exercise 6.5 Solution

### CBSE NCERT Class 7 Maths Chapter 6 Exercise 6.5 Solution in Hindi and English Medium

Class: 7 | Mathematics |

Chapter: 6 | Triangles and its Properties |

Exercise: 6.5 | English and Hindi Medium Solution |

### Class 7 Maths Chapter 6 Exercise 6.5 Solution in Videos

#### Pythagorean Triplets

Three positive integers a, b and c in the very same order are said to form a Pythagorean triplet, if c² = a² + b²

Thus, each of the triplets (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17) and (12, 35, 37) is a Pythagorean triplet.

### Class 7 Maths Exercise 6.5 Extra Questions

##### The lengths of the sides of two triangles are given below. Which of them is right angled? (i) a = 7 cm, b = 24 cm and c = 25 cm (ii) a = 8 cm, b = 5 cm and c = 10 cm

(i) Here a = 7 cm, b = 24 cm and c = 25 cm.

The largest side is c = 25 cm.

Now, a² + b² = {(7)² + (24)²} cm²

= (49 + 576) cm² = 625 cm² = (25 cm)² = c²

Or, a² + b² = c²

Or, given triangle is right-angled [by the converse of Pythagoras theorem].

(ii) Here a = 8 cm, b = 5 cm and c = 10 cm.

The largest side is c = 10 cm.

Now, a² + b² = {(8)² + (5)²} cm²

= (64 + 25) cm = 89 cm² ≠ (10)² cm²

= a² + b² ≠ c² Hence given triangle is not right-angled.

##### The two legs of a right triangle are equal and the square of its hypotenuse is 50. Find the length of each leg.

Let, length of one leg of a right angle triangle is x

Then, for a right angle triangle x² + x² = 50

So, 2x² = 50

Or, x² = 25

Or, x = 5

### Class 7 Maths Exercise 6.5 Important Questions

##### What jobs use Pythagorean Theorem?

There are many relevant applications that require the use of the Pythagorean Theorem. Engineers and astronomers use the Pythagorean Theorem to calculate the paths of spacecraft, including rockets and satellites. Architects use the Pythagorean Theorem to calculate the heights of buildings and the lengths of walls.

##### How do you reverse the Pythagorean Theorem?

In other words, the converse of the Pythagorean Theorem is the reversal of the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse: a2+b2=c2 The converse of the Pythagorean Theorem is the Pythagorean Theorem flipped.

##### How do you do Pythagorean theorem with only C?

The hypotenuse formula is simply taking the Pythagorean theorem and solving for the hypotenuse, c. Solving for the hypotenuse, we simply take the square root of both sides of the equation a² + b² = c² and solve for c. When doing so, we get c = √(a² + b²) .