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Question
AB, BC and AC are three sides of a right-angled triangle having lengths 6 cm, 8 cm and 10 cm, respectively. To verify the Pythagoras theorem for this triangle, fill in the boxes:
ΔABC is a right-angled triangle and ∠ABC = 90°.
So, by the Pythagoras theorem,
`square` + `square` = `square`
Substituting 6 cm for AB and 8 cm for BC in L.H.S.
`square` + `square` = `square` + `square`
= `square` + `square`
= `square`
Substituting 10 cm for AC in R.H.S.
`square` = `square`
= `square`
Since, L.H.S. = R.H.S.
Hence, the Pythagoras theorem is verified.
Solution
ΔABC is a right-angled triangle and ∠ABC = 90°.
So, by the Pythagoras' theorem,
AB2 + BC2 = AC2
Substituting 6 cm for AB and 8 cm for BC in L.H.S.
AB2 + BC2 = 62 + 82
= 36 + 64
= 100
Substituting 10 cm for AC in R.H.S.
AC2 = 102
= 100
Since, L.H.S. = R.H.S.
Hence, the Pythagoras theorem is verified.
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