In triangle ABC , angle B is a right angle BD is perpendicular to AC If AD = a and CD = b then AB 2 is equal to
Answers
Given : In triangle ABC , ∠B is a right angle
BD is perpendicular to AC
AD = a and CD = b
To Find : AB²
Solution:
Using geometric mean theorem
or Right angle altitude theorem
BD is geometric mean of AD and CD
=> BD = √AD.CD
=> BD =√a.b
=> BD² = ab
in Δ ADB BD ⊥ AC Hence right angle triangle
Using Pythagorean theorem
square on the hypotenuse of a right-angled triangle is
equal to the sum of the squares of the other two perpendicular sides.
AB² = AD² + BD²
=> AB² = a² + ab
=> AB² = a(a + b)
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