Triangle ADC is a isosceles triangle. if its perimeter is 80cm and AD is 30 cm ,and DC is 20 cm find AC and its area

Asked by Vaishnavi samudrala | 15th Sep, 2012, 07:44: AM

Expert Answer:

Perimeter of triangle ADC = 80 cm

So, AD + DC + AC = 80 cm

Or, 30 cm + 20 cm + AC = 80 cm

Or, 50 cm + AC = 80 cm

Or, AC = 30 cm

 

The rough sketch of this triangle can be drawn as shown below.

Here, AM is drawn perpendicular to CD.

So, MC is half of CD i.e. MC = 10 cm.

 

Using Pythagoras theorem in triangle AMC,

AM2 + MC2 = AC2

So, AM2 = AC2 - MC2 = (30 cm)2 - (10 cm)2 = 800 cm2

Or, AM = 20 cm.

 

Now, area of triangle ADC = (1/2) × CD × AM = (1/2) × 20 cm × 20  cm = 200  cm2

Answered by  | 15th Sep, 2012, 05:23: PM

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