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Question
A congruent side of an isosceles right angled triangle is 7 cm, Find its perimeter
Solution
Given: In ∆ABC, ∠ABC = 90°, AB = BC = 7 cm
To find: Perimeter of ∆ABC
In ∆ABC, ∠ABC = 90° ......[Given]
∴ AC2 = AB2 + BC2 ......[Pythagoras theorem]
∴ AC2 = (7)2 + (7)2
∴ AC2 = 49 + 49
∴ AC2 = 98
∴ AC = `sqrt(49 xx 2)` ......[Taking square root of both sides]
Perimeter of ∆ABC = AB + BC + AC
= `7 + 7 + 7sqrt(2)`
= `14 + 7sqrt(2)` cm
= `7(2 + sqrt2)`
∴ The perimeter of the given triangle is `7(2 + sqrt2)` cm
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