Do sides 7 cm, 24 cm, 25 cm form a right angled triangle ? Give reason
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 2.2 | Page 44
Do sides 7 cm, 24 cm, 25 cm form a right angled triangle ? Give reason
In the triplet (7, 24, 25),
72 = 49, 242 = 576, 252 = 625 and 49 + 576 = 625
The square of the largest number is equal to the sum of the squares of the other two numbers.
∴ Sides 7 cm, 24 cm, 25 cm form a right angled triangle.
Explanation:-
Yes, the sides 7 cm, 24 cm, and 25 cm form a right-angled triangle.
We can use the Pythagorean theorem to verify this. According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the hypotenuse is the side with length 25 cm, and the other two sides have lengths 7 cm and 24 cm. So we have:
25^2 = 7^2 + 24^2 625 = 49 + 576 625 = 625
The equation is true, so the sides 7 cm, 24 cm, and 25 cm satisfy the Pythagorean theorem, and thus form a right-angled triangle.
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 2.2 | Page 44