in a triangle ABC D and e are points on a b and ac respectively such that DE is parallel BC if a b is equals to 2.4 cm is equal to 3.2 cm is equal to 2 cm and BC is equal to 5 centimetre find BD and CE
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Well if you cant understand my previous answer,Given: ΔABC, D and E are points on sides AB and AC respectively. Also, DE||BC and AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm. To Find: BD and CE Find:
refer to image... and then
⇒ AC = 8 cm and AB = 6 cm BD = AB AD = 6 cm 2.4 cm = 3.6 cm CE = AC AE = 8 cm 3.2 cm = 4.8 cm Thus, the BD and CE are 3.6 cm and 4.8 cm respectively
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Answer:
heya✔️✔️
Step-by-step explanation:
GIVEN: In Δ ABC, D and E are points on AB and AC , DE || BC and AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BE = 5 cm.
In Δ ADE and Δ ABC,
∠ADE =∠ABC (corresponding angles)
[DE || BC, AB is transversal]
∠AED =∠ACB (corresponding angles)
[DE || BC, AC is transversal]
So, Δ ADE ~ Δ ABC (AA similarity)
Therefore, AD/AB = AE/AC = DE/BC
[In similar triangles corresponding sides are proportional]
AD/AB = DE/BC
2.4/(2.4+DB) = 2/5
2.4 × 5 = 2(2.4+ DB)
12 = 4.8 + 2DB
12 - 4.8 = 2DB
7.2 = 2DB
DB = 7.2/2
DB = 3.6 cm
Similarly, AE/AC = DE/BC
3.2/(3.2+EC) = 2/5
3.2 × 5 = 2(3.2+EC)
16 = 6.4 + 2EC
16 - 6.4 = 2EC
9.6 = 2EC
EC = 9.6/2
EC = 4.8 cm
Hence,BD = 3.6 cm and CE = 4.8 cm.
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