Question

In a triangle ABC BD is perpendicular to AC,BC=60 and BD=36,Find the area of ABC

Answer 1

CORRECT QUESTION :

In a triangle ABC BD is perpendicular bisector of AC . BC=60 and BD=36,Find the area of ABC

Answer:

area ( ∆ ABC ) = 1728 cm²

Step-by-step explanation:

GIVEN :

A ∆ ABC with BD perpendicular to AC.

BC = 60 cm ,

Perpendicular to AC, BD = 36 cm

We get a right angle ∆ BDC right angled at D

In rt. ∆ BDC ,

We have Perpendicular BD = 36 cm

Hypotenuse BC = 60 cm

As , Base or rt. ∆ = √(Hypotenuse ² - Perpendicular ²)

So, Base DC = √(60² - 36²) = 48 cm

So, DC is 48 cm.

As no other data given let's assume

BD bisects AC

So, AC = 2 DC = 2 x 48 = 96 cm

We know that;

Area of a traingle = ½ x Base x Height

So, area ( ∆ ABC ) = ½ x AC x BD

= ½ x 96 x 36 cm²

= 1728 cm²

Hence, area ( ∆ ABC ) = 1728 cm²