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Q.

If DE∥BC and AD = 1.7cm, AB = 6.8cm and AC = 9cm. Then length of AE is _____.

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a

2.25 cm

b

4.5 cm

c

3.4 cm

d

5.1 cm

answer is A.

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Detailed Solution

seo

In ΔADE and ΔABC
∠ABC = ∠ADE (alternate exterior angles)
∠ACB = ∠AED (alternate exterior angles)
∠A = ∠A (common)
Therefore, ΔADE ∼ ΔABC by AAA criterion.
Hence now we will compare the length of corresponding sides of both the triangles we get:

\frac{AD}{AB}

=

\frac{AE}{AC}

..............(1)
Since it is given that:
AD = 1.7cm
AB = 6.8cm
AC = 9cm
Therefore, putting the respective values in equation 1 we get:
⇒

\frac{1.7}{6.8}

=

\frac{AE}{9}

⇒

\frac{AE}{9}

=

\frac{1}{4}

⇒ AE =

\frac{9}{4}

cm
⇒ AE = 2.25cm
Hence, option (1) is the correct option.

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If DE∥BC and AD = 1.7cm, AB = 6.8cm and AC = 9cm. Then length of AE is _____.