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Question
From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `2sqrt(2)` then l (AB) = ?
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Solution
AB = BC ......[Given]
∴ ∠A = ∠C ......[Isosceles triangle theorem]
Let ∠A = ∠C = x ......(i)
In ∆ABC, ∠A + ∠B + ∠C = 180° ......[Sum of the measures of the angles of a triangle is 180°]
∴ x + 90° + x = 180° ......[From (i)]
∴ 2x = 90°
∴ x = `90^circ/2` ......[From (i)]
∴ x = 45°
∴ ∠BAC = ∠BCA = 45°
∴ ∆ABC is a 45° – 45° – 90° triangle.
∴ AB = BC = `1/sqrt(2) xx "AC"` ......[Side opposite to 45°]
= `1/sqrt(2) xx 2sqrt(2)`
∴ `l("AB")` = 2 units
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