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In an Isosceles Triangle Abc, Ab = Ac = 25 Cm, Bc = 14 Cm. Calculate the Altitude from a on Bc. - CBSE Class 10 - Mathematics

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Question

In an isosceles triangle ABC, AB = AC = 25 cm, BC = 14 cm. Calculate the altitude from A on BC.

Solution

We have

AB = AC = 25 cm and BC = 14 cm

In ΔABD and ΔACD

∠ADB = ∠ADC [Each 90°]

AB = AC [Each 25 cm]

AD = AD [Common]

Then, ΔABD ≅ ΔACD [By RHS condition]

∴ BD = CD = 7 cm [By c.p.c.t]

In ΔADB, by Pythagoras theorem

AD2 + BD2 = AB2

⇒ AD2 + 72 = 252

⇒ AD2 = 625 − 49 = 576

⇒ AD = `sqrt576` = 24 cm

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Solution In an Isosceles Triangle Abc, Ab = Ac = 25 Cm, Bc = 14 Cm. Calculate the Altitude from a on Bc. Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle.
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