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°

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.