Question

Q. 8: 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





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Answer 1

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Answer:

Question:

Q. 8: 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

Solution:

(i)

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 a right-angled triangle.

Length of Hypotenuse = 25 cm

___________________________

(ii)

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, 32 + 62 ≠ 82

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 satisfy Pythagoras theorem.

I Hope It Helps You✌️

Answer 2

Answer:-

i) perpendicular - 24cm

hypotenuse - 25cm

base- 7cm

H2 = P2 +B2

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

625= 576+49

625=625

Therefore, it is a right triangle

ii) perpendicular - 6cm

hypotenuse - 8cm

base - 3cm

H2 = P2 + B2

(8)2= (6)2 + (3)2

64 = 36 + 9

64 is not equal to 45

Therefore, it is not a right triangle