Question
Download Solution PDFIn ΔABC, MN∥BC, the area of quadrilateral MBCN = 130 cm2. If AN : NC = 4 : 5, then the area of ΔMAN is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven,
the area of quadrilateral MBCN = 130 cm2.
AN : NC = 4 : 5
Hence, AC = 4 + 5 = 9
In ΔABC, If MN∥BC, then
Area of ΔAMN/area of ΔABC = (AN/AC)2
Area of ΔAMN/area of ΔABC = (4/9)2 = 16/81
Area of ΔAMN = 16 unit and area of ΔABC = 81 unit
Now, Area of quadrilateral MBCN = area of ΔABC - area of ΔAMN
⇒ 81 - 16 unit = 130 cm2
⇒ 65 unit = 130 cm2
⇒ 1 unit = 130/65 = 2 cm2
∴ Area of ΔAMN = 16 × 2 = 32 cm2
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