Question

In TriangleABC, AB = 7 cm, AC = 9 cm. Point D is on AB,
such that BD = 3 cm. DE is drawn cutting AC at E
so that quadrilateral BCED has 5/7 the area of TriangleABC.
Find AE.

Pls write full solution and as early as possible.​

Answer 1

AE = 4.5 cm if In ΔABC, AB = 7 cm, AC = 9 cm. Point D is on AB, such that BD = 3 cm. DE is drawn cutting AC at E so that quadrilateral BCED has 5/7 the area of Δ ABC.

Step-by-step explanation:

Area of ΔADE = Area of ΔABC - Area of Quadrilateral BCED

Let say Area of ΔABC  = 7x

=> Area of ΔADE = 7x - (5/7)7x  = 2x

Lets draw ⊥ from C & E at AB at M & N point respectively

Area of Δ ABC = (1/2) * AB * CM  = 7x

Area of Δ ADE = (1/2) * AD * EN = 2x

AB = 7 cm   AD  = 7-3 = 4 cm

=>  7 * CM / (4 * EN)  = 7/2

=> CM = 2 EN

=> EN / CM = 1/2

ΔANE ≈ ΔAMC

AE/AC  = EN/CM

=> AE / AC = 1/2

=> AE = AC/2

=> AE = 9/2

=> AE = 4.5 cm

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Answer 2

4.5 cm

Step-by-step explanation:

I hope you understand