AD is a median of triangle ABC and area of ∆ ADC =15𝑐𝑚2, then ar(∆ ABC) isa) 15 𝑐𝑚2 b) 22.5𝑐𝑚2 c) 30 𝑐𝑚2 d) 37.5 𝑐𝑚2
Question
AD is a median of triangle ABC and area of ∆ ADC =15𝑐𝑚2, then ar(∆ ABC) isa) 15 𝑐𝑚2 b) 22.5𝑐𝑚2 c) 30 𝑐𝑚2 d) 37.5 𝑐𝑚2
Solution
In a triangle, the median divides it into two triangles of equal areas.
Given that AD is a median of triangle ABC, it means that the area of triangle ADC is equal to the area of triangle ADB.
Since the area of triangle ADC is given as 15 cm², the area of triangle ADB is also 15 cm².
Therefore, the total area of triangle ABC (which is the sum of the areas of triangle ADC and triangle ADB) is 15 cm² + 15 cm² = 30 cm².
So, the correct answer is c) 30 cm².
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