In a triangle ABC, let E be the midpoint of AC and F be the midpoint of AB. The medians BE and CF in

Question

In a triangle ABC, let E be the midpoint of AC and F be the midpoint of AB. The medians BE and CF intersect at G. Let Y and Z be the midpoints of BE and CF respectively. If the area of triangle ABC is 480, find the area of triangle CYZ.

Accepted Answer

{"content":[{"content":[{"text":"Step 1:","type":"text","marks":[{"type":"bold"}]},{"text":" Let BE = 6x","type":"text"}],"type":"paragraph"},{"type":"paragraph","content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 2:"},{"type":"text","text":" area (GYZ )  1 "}]},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3:","type":"text"},{"text":" area (GBC )  4 ","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 4:","type":"text"},{"text":" Area(GBC) = 16(area of GYZ)","type":"text"}],"type":"paragraph"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 5:"},{"text":" 1                480","type":"text"}],"type":"paragraph"},{"content":[{"text":"Step 6:","type":"text","marks":[{"type":"bold"}]},{"type":"text","text":" area of GBC =      of area(ABC) =     = 160"}],"type":"paragraph"},{"content":[{"text":"Step 7:","type":"text","marks":[{"type":"bold"}]},{"text":" 3                 3","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 8:","type":"text"},{"text":" area of GYZ = 10","type":"text"}],"type":"paragraph"}],"type":"doc"}

Guide / Hint

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