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Question
The sides of certain triangles are given below. Determine which of them right triangles are.
(a – 1) cm, `2sqrta` cm, (a + 1) cm
Solution
P = (a-1) cm, q = `2sqrta` 𝑐𝑚 𝑎𝑛𝑑 𝑟=(𝑎+1)𝑐𝑚
Then,
`p^2+q^2=(0a-1)^2+(2sqrta)^2`
=`a^2+1-2a+4a`
=`a^2+1+2a`
=`(a+1)^2`
`r^2=(a+1)^2`
`p^2+q^2=r^2`
Thus, the given triangle is right-angled.
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