Question

In an isosceles Triangle ABC, AB = AC = 10cm, AD⊥ BC and AD = 8cm. Find the length of BC?

Answer 1

Answer:

BC = 12 cm

Step-by-step explanation:

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Answer 2

Answer:

AB=AC=10cm

AD is perpendicular to BC

In right triangle ADB,

AB square = AD square + BD square

(By pythagoras theorem)

So, 10×10 = 8×8 + BD square

100-64 = BD square

BD square = 36

BD = 6cm

In triangle ABD and ACD,

/_ADB=/_ADC=90 degrees (as AD is perpendicular to BC) (right angle)

AB=AC (Given)

AD=AD (Common side)

So, triangle ABD is congruent to triangle ACD

(By RHS congruency criterion)

So BD=CD (By CPCT)

BD=CD=6cm

So, BD+CD=BC

BC=12cm

Hence, the length of BC is 12cm.

Step-by-step explanation:

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