In △abc, point d∈ ab with ad: db=5: 3, point e∈ bc so that be: ec=1: 4. if aabc=40 in2, find aadc, abdc, and acde.

1. If AD : DB = 5 : 3, then AD = 5x in and DB = 3x in.

2. If BE : EC = 1 : 4, then BE = y and EC = 4y.

3. Consider ΔABc. The area of this triangle is

where is the heigth drawn to the side AB.

Since AB = AD + DB = 5x + 3x = 8x, you have that

4. Consider ΔADC. The area of this triangle is

5. Consider ΔBDC. The area of this triangle is

On the other hand,

6. Consider ΔCDe. The area of this triangle is

Area of  .

Area of the triangle is ,

Δ

where is height on side

Now,

Now,

Now,

where is height on side

Now consider Δ

Hence, Area of .

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eve and marks ratios are equivalent

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