Ex 6.5, 4 Which of the following can be the sides of a right triangle? (i) 2.5 cm,6.5 cm, 6 cm. In the case of right-angled triangles, identify the right angles. Given sides,
2.5 cm, 6.5 cm, 6 cm
We know that,
Hypotenuse is the largest side.
So, Hypotenuse = 6.5 cm
Checking Pythagoras Theorem
〖(𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒)〗^2 = 〖(𝐵𝑎𝑠𝑒)〗^2 + 〖(𝑃𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟)〗^2
〖(𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒)〗^2
= 〖(6.5)〗^2
= (65/10)^2
= 4225/100
= 42.25
〖(𝐵𝑎𝑠𝑒)〗^2 + 〖(𝑃𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟)〗^2
= 〖(2.5)〗^2 + 〖(6)〗^2
= (25/10)^2 + 36
= 625/100 + 36
= (625 + 3600)/100
= 4225/100
= 42.25
Since L.H.S = R.H.S
Pythagoras theorem is satisfied
Hence, 2.5 cm, 6.5 cm, 6 cm form sides of a right triangle
While making ∆ABC,
right angle should be opposite Hypotenuse side
Hence ∠ B = 90°

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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