In ΔABC, AD is a median and P is a point on AD such that AP : PD = 3 : 4. Then ar(ΔBPD) : ar(ΔABC) is equal to:
Show answer & explanation
Correct answer: D
Explanation
Correct Answer is option 4 i.e. 2 : 7
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Concept |
Understanding |
Application |
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Median divides a triangle in two equal parts. |
Hence, area ΔADB = area ΔADC AP : PD = 3 : 4 |
In ΔABD ⇒ area ΔBPD/ area ΔAPB = DP/AP ⇒ area ΔBPD/ area ΔAPB = 4/3 Let the area of ΔBPD be 4 unit So, area of ΔAPB will be = 3 unit So, area of ΔBAD = area ΔBPD + area ΔAPB = 4 + 3 = 7 unit Area of ΔABC = 2 × area ΔBAD = 2 × 7 = 14 unit Hence, required ratio = 4 : 14 = 2 : 7 |