∆ABC is an isosceles triangle with AB = AC = 13cm and the length of altitude from A on BC is 5cm. Then, BC = ? (a) 12cm (b) 16cm (c) 18cm (d) 24cm
∆ABC is an isosceles triangle with AB = AC = 13cm and the length of altitude from A on BC is 5cm. Then, BC = ? (a) 12cm (b) 16cm (c) 18cm (d) 24cm

Correct Answer: (d) 24 cm

Explanation:

 

 

In triangle ABC,

Let the altitude from A on BC meets BC at D.

AD = 5 cm

AB = 13 cm

D is the midpoint of BC

Applying Pythagoras theorem in right-angled triangle ABD,

????????2 = ????????2 + ????????2

????????2 = ????????2 − ????????2

????????2 = 132 − 52

????????2 = 169 − 25

????????2 = 144

???????? = √144 => 12 ????????

BC = 2BD => 24 cm