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Question
If the sides of a triangle are in the ratio 5 : 12 : 13 then, it is ________
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Solution
a right angled triangle
Explanation;
Hint:
132 = 169
52 = 25
122 = 144
169 = 25 + 144
∴ 132 = 52 + 122
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In ∆LMN, l = 5, m = 13, n = 12 then complete the activity to show that whether the given triangle is right angled triangle or not.
*(l, m, n are opposite sides of ∠L, ∠M, ∠N respectively)
Activity: In ∆LMN, l = 5, m = 13, n = `square`
∴ l2 = `square`, m2 = 169, n2 = 144.
∴ l2 + n2 = 25 + 144 = `square`
∴ `square` + l2 = m2
∴ By Converse of Pythagoras theorem, ∆LMN is right angled triangle.
