Q. 14.2( 135 Votes )

Sides of triangle

Answer :

(i) Given: sides of the triangle are 7 cm, 24 cm, and 25 cm

Squaring the lengths of these sides, we get: 49, 576, and 625.


49 + 576 = 625


Or, 72 + 242 = 252


The sides of the given triangle satisfy Pythagoras theorem


Hence, it is a right triangle


We know that the longest side of a right triangle is the hypotenuse


Therefore, the length of the hypotenuse of this triangle is 25 cm


(ii) It is given that the sides of the triangle are 3 cm, 8 cm, and 6 cm


Squaring the lengths of these sides, we will obtain 9, 64, and 36


However, 9 + 36 ≠ 64


Or, 32 + 62 ≠ 82


Clearly, the sum of the squares of the lengths of two sides is not equal to the square of the length of the third side


Therefore, the given triangle is not satisfying Pythagoras theorem


Hence, it is not a right triangle


(iii)Given that sides are 50 cm, 80 cm, and 100 cm.


Squaring the lengths of these sides, we will obtain 2500, 6400, and 10000.


And, 2500 + 6400 ≠ 10000


Or, 502 + 802 ≠ 1002


Now, the sum of the squares of the lengths of two sides is not equal to the square of the length of the third side


Therefore, the given triangle is not satisfying Pythagoras theorem


Hence, it is not a right triangle


(iv)Given: Sides are 13 cm, 12 cm, and 5 cm


Squaring the lengths of these sides, we get 169, 144, and 25.


Clearly, 144 +25 = 169


Or, 122 + 52 = 132


The sides of the given triangle are satisfying Pythagoras theorem


Therefore, it is a right triangle


We know that the longest side of a right triangle is the hypotenuse


Therefore, the length of the hypotenuse of this triangle is 13 cm

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