Question

In the given figure, DE || BD. Determine AC and AE.

Answer 1

SOLUTION :  

Given : DE || BD

AB = 4cm , BC = 15cm , DE = 12cm , AD= 14 cm

In ∆ADE &  ∆ ACB,  

∠ADE = ∠C  (corresponding angles as  DE || BD)

∠A = ∠A (Common)

∆ADE ∼ ∆ACB

[By AA Similarity]

AE/ AB = DE/CB = AD/AC

[since Triangles are similar, hence corresponding sides will be proportional]

AE/4 = 12/15 = 14/AC

AE/4 = 12/15

15× AE = 12 × 4

AE = (12 × 4)/15

AE =( 4 × 4) /5

AE = 16/5

12/15 = 14/AC

12 × AC = 15 × 14

AC = (15×14)/12

AC = (5 × 14)/4

AC = 35/2

Hence, the value of AE is 16/5 & AC is 35/2.

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Answer 2

Answer:

AC = 35/2 AE = 16/5

Step-by-step explanation:

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