Using Pythagoras theorem determine the length of AD in terms of b and

1.	Using Pythagoras theorem determine the length of AD in terms of b and c shown in Fig.
Answer» We have, In ∆BAC, by Pythagoras theorem, we have BC² = AB² + AC² ⇒ BC² = c² + b² ⇒ BC = √(c² + b²) In ∆ABD and ∆CBA ∠B = ∠B [Common] ∠ADB = ∠BAC [Each 90°] Then, ∆ABD ͏~ ∆CBA [By AA similarity] Thus, \(\frac{AB}{CB} = \frac{AD}{CA}\) [Corresponding parts of similar triangles are proportional] \(\frac{c}{\sqrt{(c^2 + b^2)}}\) = \(\frac{AD}{b }\) ∴ AD = \(\frac{bc}{\sqrt{(c^2 + b^2)}}\)

Using Pythagoras theorem determine the length of AD in terms of b and c shown in Fig.

Answer»

We have,

In ∆BAC, by Pythagoras theorem, we have

BC² = AB² + AC²

⇒ BC² = c² + b²

⇒ BC = √(c² + b²)

In ∆ABD and ∆CBA

∠B = ∠B [Common]

∠ADB = ∠BAC [Each 90°]

Then, ∆ABD ͏~ ∆CBA [By AA similarity]

Thus, \(\frac{AB}{CB} = \frac{AD}{CA}\) [Corresponding parts of similar triangles are proportional]

\(\frac{c}{\sqrt{(c^2 + b^2)}}\) = \(\frac{AD}{b }\)

∴ AD = \(\frac{bc}{\sqrt{(c^2 + b^2)}}\)