Question

A congruent side of an isosceles right angled triangle is 7 cm, Find its perimeter

Answer 1

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