Question

ΔАВС is an isosceles triangle in which AB = AC = 17 cm and BC = 16 cm. Find the length of perpendicular drawn from A to BC.

Answer 1

Given: ΔABC is isosceles with AB = AC = 17 cm and BC = 16 cm.

Step-wise calculation:

1. In an isosceles triangle

The perpendicular from apex A to base BC bisects the base. 

So, BD = DC

= `16/2`

= 8 cm

2. In right triangle ABD,

AB is the hypotenuse 17 cm and BD = 8 cm.

So, `AD = sqrt(AB^2 - BD^2)`

= `sqrt(17^2 - 8^2)`

= `sqrt(289 - 64)`

= `sqrt(225)`

= 15 cm

The length of the perpendicular from A to BC is 15 cm.