Question

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In the given figure, AP = 3cm , AR = 4.5cm , AQ = 6cm , AB = 5cm , AC = 10cm . Find AD .


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Answer 1

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From the info we get

AB/AP=AC/AQ (in ∆ ABC)

by using converse of BPT theoram

PQ||BC

And in ∆ ABD PR||BD

AD= AR+ RD

AD= 4.5+ x

AB/AP = AD/AR

$( \frac{5}{3} ) = \frac{4.5 + x}{4.5 } \\ \frac{5 \times 4.5}{3} = 4.5 + x \\ 7.5 = 4.5 + x \\ x = 3$

here, length of AD =4.5+x

AD = 7.5 answer

$\huge\fbox\red{ ♡ AD=7.5 }$

Answer 2

From the given Diagram we get,

• (AB/AP) = (AC/AQ)

$\huge\underline\mathrm{SoLuTion:-}$

In triangle ABC, (AB/AP) = (AC/AQ)

By using converse of “Thales theorem” PQ is parallel to BC.

• RD = x

In triangle ABD, PR is parallel to BD

AD = AR + RD

AD = 4.5 + x

(AB/AP) = (AD/AR)

(5/3) = (4.5 + x)/4.5

(5 x 4.5)/3 = 4.5 + x

7.5 = 4.5 + x

x = 7.5 – 4.5

x = 3

Here we need to find the length of AD = 4.5 + x

                                                       = 4.5 + 3

                                                       = 7.5 cm

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Hope This Helps :)