Question

in triangle ABC,AD is perpendicular to BC if BD/DC=3/2 then the area of triangle ABC /area of triangle ADC

Answer 1

Answer:

5/2

Step-by-step explanation:

assume BD=3x & DC =2x

area of ABC = 1/2 × 5x × AD

area of ADC = 1/2 × 2x × AD

then,

we get,

5/2

Answer 2

area of ΔABC / area of ΔABD = 5/3

Given,

AD ⊥ BC

BD/DC = 3/2

To Find,

area of triangle ABC / area of triangle ADC

Solution,

We can solve this problem using a simple method.

We have been given a triangle ΔABC.

In this triangle, let the base be BC.

We have also been given that AD ⊥ BC.

This means that AD is the altitude of the triangle ΔABC.

We have also been given that BD/DC = 3/2.

⇒ BD = 3x and DC = 2x

where x is a constant.

Now, the area of a triangle is given by:

⇒ area = 1/2 × base × altitude

Consider ΔABC:

base = BC

⇒ base = BD + DC

⇒ base = 3x + 2x

⇒ base = 5x

altitude = AD

area of ΔABC = 1/2 × 5x × AD

Consider ΔABD:

⇒ base = BD

⇒ base = 3x

altitude = AD

area of ΔABD = 1/2 × 3x × AD

area of ΔABC / area of ΔABD = (1/2 × 5x × AD) / (1/2 × 3x × AD)

⇒ area of ΔABC / area of ΔABD = 5/3

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