Question

in th triangle shown, what is the perpendicular distance from the top vertex to the bottom side? What is the area of the triangle ?​

Answer 1

Answer:

$AB = AC = 4cm \\ \\ ΔABC \: is \: a \: isoceless \: triangle. \: \\ <ABD+ <ACD+<BAC=180° \\ <ABD = <ACD = \frac{180 - 120}{2} = 30° \\ Consider \: ΔABD \: \\ <ADB=90° \\ <BAD=180-(30+90) = 60°$

The sides of the right angle triangle with angles 30°, 60°, 90° are proportional to the number 1 : √3 : 2

AD : BD : AB = 1 : √3 : 2

AB = 2x = 4cm

x = 2 cm

AD = 2 cm

BD = 2√3cm

Perpendicular distance from the top vertex to the bottom side = AD = 2 cm

BC = 2BD = 4√3 cm

Area of triangle = 1/2 bh

1/2 × 4√3 × 2 = 4√3 cm^2