Question

In the figure, if ∆ABC ~ ∆PQR, find the value of x?

Answer 1

Two Triangles are said to be similar if their i)corresponding angles are equal and ii)corresponding sides are proportional.(the ratio between the lengths of corresponding sides are equal)

•Similarity of triangles should be expressed symbolically using correct correspondence of their vertices.

GIVEN:
∆ABC ~  ∆PQR
AB =6 cm  , BC = 4 cm , PQ = 4.5 cm , QR= x cm

AB /PQ = BC/QR
[corresponding sides of similar triangles are proportional]

6/4.5 = 4/x
4.5 x = 6× 4
x = (4.5× 4)/6
x = (4.5 × 2 )/3 = 1.5 × 2
x = 3 cm

Hence, the value of x is 3 cm.

HOPE THIS WILL HELP YOU...

Answer 2

if 2 triangles are similar then their sides are in same ratio
∆ABC ~ ∆PQR
AB/PQ=BC/QR=AC/PR
AB/PQ=BC/QR
6/4.5=4/X 
6*X=4.5*4
X=18/6
X=3