In △abc, point d∈ ac with ad: dc=4: 3, point e∈ bc so that be: ec=1: 5. if acde=5 in2, find abdc, aabd, and aabc.

ar ΔBDC=6

ar ΔABD=8

ar ΔABC=14

Explanation:

Please take a look of attach figure.

We are given area of triangle ar ΔCDE=5

ar ΔCDE=------------(1)

ar ΔBDE=------------(2)

Divide eq(2) by eq(1) and we get,

So, ar ΔBDE=1

ar ΔBDC=ar ΔBDE+ ar ΔCDE

ar ΔBDC=1+5 = 6

Similarly,

ar ΔABD=8

ar ΔABC=ar ΔABD + ar ΔBDC

ar ΔABC=8+6 = 14

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