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
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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