Question

In triangle ABC DE parallel to BC if ad equal to 5 cm BD equal to 7 cm and AC equal to 18 cm find the length of AE

Answer 1

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Answer 2

Answer:

Length of AE = 7.5 cm

Step-by-step explanation:

For better explanation of the solution, see the attached figure of the problem :

Given : DE ║ BC , AD = 5 cm , BD  7 cm , AC = 18 cm

To find : Length of AE

Solution : In ΔADE and ΔABC

∠ADE = ∠ABC ( Corresponding angles are equal)

∠A = ∠A ( Common angles are equal)

So, By AA postulate of similarity of triangles, ΔADE ~ ΔABC

Since, The corresponding sides of the similar triangles are proportional to each other

$\implies \frac{AD}{AB}=\frac{AE}{AC}\\\\\implies\frac{5}{12}=\frac{AE}{18}\\\\\implies AE\times 12=5\times 18\\\\\implies AE=\frac{90}{12}\\\\\implies AE=7.5\:\:cm$

Hence, Length of AE = 7.5 cm