ABC is right angled at B. BD is perpendicular upon AC. If AD =a, CD=b,then (AB)square=?
Answers
angle A = angle A (common)
angle ABC = angle ADB (each 90°)
therefore using AA similarity
In ∆ABC ~ ∆ADB
using CPST
AB/AC = AD/AB
ABsq = AD×AC
ABsq = a(a+b)
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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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