Question

37) In an isosceles ABC, If AB=AC = 13 cm and the altitude from A on BC is 12
cm., then length of BC is:
(a) 10 cm
(b) 8cm
(C) 12 cm
(d) None of these​

Answer 1

Answer:

a)10 cm

Step-by-step explanation:

In ∆ABC, AB=AC=13 cm

and altitude from A on BC =12

Now using Pythagoras Theorem,

In ∆ABD,

AB^2=AD^2+BD^2

(13)^2=(12)^2+BD^2

169=144+ BD^2

BD^2=169-144

BD^2=25

BD=√25

BD= 5 cm ------------(1)

Similarly,

In ∆ACD,

AC^2=AD^2+DC^2

(13)^2=(12)^2+DC^2

169=144+DC^2

DC^2=169-144

DC^2=25

DC=√25

DC=5 cm -----------(2)

Since,∆ABC is an isosceles triangle

then,

BC=BD+BC

from equation (1) & (2),

BC=(5+5) cm

BC=10 cm