# On the side AB of triangle ABC, point D is taken in such a way that AD: DB = 5: 1. On the BC side, point E is taken

May 30, 2021 | education

| **On the side AB of triangle ABC, point D is taken in such a way that AD: DB = 5: 1. On the BC side, point E is taken, dividing the BC side in half. The area of triangle DBE is known to be 18. Calculate the area of triangle ABC.**

If point E is in the middle of the BC side, then it can be argued that the height of the BCA triangle, lowered to the base of the BA, is twice the height of the BED triangle. If sides AD and BD are in a 5: 1 ratio, then the bases of triangles BA and BD are in a 6: 1 ratio.

Triangle area BED = 18 cm2. Then the area of a triangle, which has 2 times the height and 6 times the base, will be 12 times larger.

S = 18 * 12 = 216 cm2.

Answer: 216 cm2.

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