Sides of triangles are given below. Determine which of them are right triangles. In case of a rig

Question 1

Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.

(i) 7 cm, 24 cm, 25 cm

(ii) 3 cm, 8 cm, 6 cm

(iii) 50 cm, 80 cm, 100 cm

(iv) 13 cm, 12 cm, 5 cm

Solution:

(i) 7 cm, 24 cm, 25 cm

Given, sides of the triangle are 7 cm, 24 cm, and 25 cm

Squaring the lengths of the sides of the, we will get 49, 576, and 625

49 + 576 = 625

$(7)^2 + (24)^2 = (25)^2$

Therefore, the above equation satisfies, Pythagoras theorem. Hence, it is right angled triangle

Length of Hypotenuse = 25 cm

(ii) 3 cm, 8 cm, 6 cm

Given, sides of the triangle are 3 cm, 8 cm, and 6 cm

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

Clearly, 9 + 36 ≠ 64

Or, $3^2 + 6^2 ≠ 8^2$

Therefore, the sum of the squares of the lengths of two sides is not equal to the square of the length of the hypotenuse

Hence, the given triangle does not satisfies Pythagoras theorem

(iii) 50 cm, 80 cm, 100 cm

Given, sides of triangle’s are 50 cm, 80 cm, and 100 cm

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

However, 2500 + 6400 ≠ 10000

Or, $50^2 + 80^2 ≠ 100^2$

As you can see, 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 does not satisfies Pythagoras theorem

Hence, it is not a right triangle

(iv) 13 cm, 12 cm, 5 cm

Given, sides are 13 cm, 12 cm, and 5 cm

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

Thus, 144 +25 = 169

Or, $12^2 + 5^2 = 13^2$

The sides of the given triangle are satisfying Pythagoras theorem

Therefore, it is a right triangle

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

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