Question

∆PQR~∆XYZ and the perimeters of ∆PQR and ∆XYZ are 30cm and 18cm respectively. If QR= 9cm then YZ= ?
12.5 cm
9.5 am
5.4 cm
4.5 cm​

Answer 1

Answer:

IF PQR IS SIMILAR TO XYZ THEN RATIOS OF ALL CORRRESPONDING DIMENSIONS ARE EQUAL SO PERIMETER 30/18=QR/YZ SO THAT 30/18=9/YZ----------------------YZ=9*18/30------------------------------YZ=5.4

Step-by-step explanation:

Answer 2

Given: ∆PQR~∆XYZ. and the perimeters of ∆PQR and ∆XYZ are $30$cms. and 18cm.

QR= 9cm then we have to find YZ.

The given problem is solved in the following way;

Here, both the triangles are the same.

Let assume perimeters of the both triangles are$P_{1} and P_{2}$.

Also, $QR=9cm. P_{1}=30cm. and P_{2}=18cm.$

Then,

$=>\frac{PQ}{XY} =\frac{QR}{YZ} =\frac{PR}{XZ} =\frac{P_{1} }{P_{2} }$

[∵ Ration of corresponding sides of similar triangles is equal to the ratio of their perimeters]

$=>\frac{QR}{YZ} =\frac{P_{1} }{P_{2} } \\\\=>\frac{9}{YZ} =\frac{30}{18} \\\\=>\frac{9*18}{30} =YZ\\\\=>YZ=5.4cm.$

Hence, $YZ=5.4cm.$