Question

In SABC PQR, find PR.
2 som
4cm
B​

Answer 1

Answer:

In triangle ABC and triangle PQR we have :

\frac{AB}{PQ}=\frac{4}{6}=\frac{2}{3}

PQ

AB

=

6

4

=

3

2

\frac{BC}{QR}=\frac{7}{10.5}=\frac{70}{105}=\frac{2}{3}

QR

BC

=

10.5

7

=

105

70

=

3

2

<B=<Q so the two triangles are similar by SAS therem.In similar triangles sides are in proportion.

a)Let PR=x.AC=8cm .Forming the proportion in similar triangles :

\frac{4}{6}=\frac{8}{x}

6

4

=

x

8

Cross multiplying:

4x=48 or x=12.

b) In similar triangles the ratio of area is equal to square of ratio of proportional sides.

\frac{Area of triangle ABC}{Area of triangle PQR}=(\frac{4}{6} )^{2}=\frac{16}{36}=\frac{4}{9}

AreaoftrianglePQR

AreaoftriangleABC

=(

6

4

)

2

=

36

16

=

9

4

Step-by-step explanation:

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