Question

In triangle ABC and triangle PQR, AB=4cm, BC=7cm, PQ=6cm, QR=10.5cm and m angle B=m angle Q. find PR if AC= 8cm

Answer 1

In triangle  ABC and triangle PQR we have :

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

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

<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 :

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

Cross multiplying:

4x=48 or x=12.

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

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

Answer 2

Step-by-step explanation:

In triangle ABC and triangle PQR

AB/PQ=4/6=2/3

therefore BC/QR=7/10.5=70/105=2/3

angleB= angleQ so tei triangle are similar by SAS.

a)Let PR=x,AC=8cm

therefore 4/6=8/x

4x=48

x=12

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

Area of triangle ABC/Area of triangle PQR=(4/6)^2

=16/36

=4/9

Hope this helps u