NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5

(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.

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

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.

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.

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) .