Question

hiiii!!!!!
please solve

Answer 1

Answer:

25: 4

Step-by-step explanation:

Given that DE is // to AC

Prove that ΔEBE is similar to ΔABC:

∠BED = ∠BCA (corresponding angles)

∠BDE = ∠BAC  (corresponding angles)

∠DBE = ∠ABC (common angles)

By property of AAA, ΔDBE is similar to ΔABC

Find the scale factor of ΔABC to ΔBDE:

Since ΔABC is similar to ΔBDE

Scale Factor = AB / DB

Scale Factor = (2 + 3) / 2 = 5/2

Find the ratio of area to ΔABC: ΔBDE

Ratio  of area  ΔABC: ΔBDE= (5/2)²

Ratio  of area  ΔABC: ΔBDE= 25/4

Answer: The ratio of area ΔABC: ΔBDE is 25 : 4

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ALETERNATIVE SOLUTION:

Prove that ΔEBE is similar to ΔABC:

∠BED = ∠BCA (corresponding angles)

∠BDE = ∠BAC  (corresponding angles)

∠DBE = ∠ABC (common angles)

By property of AAA, ΔDBE is similar to ΔABC

Find the ratio of area to ΔABC: ΔBDE

Area1/Area2 = (Length1/Length2)²

Area1/Area2 = (5/2)²

Area1/Area2 = 25/4

Answer: The ratio of area ΔABC: ΔBDE is 25 : 4