pqr is similar to xyz what is the perimeter of xyz? A.21cm B.63cm C. 105cm D.126cm

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smncen2010 smncen2010

05-02-2020
Mathematics

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pqr is similar to xyz what is the perimeter of xyz? A.21cm B.63cm C. 105cm D.126cm

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calculista calculista · Answer 1 · 2020-02-11T18:06:26+01:00

Answer:

option D. 126 cm

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

Triangles PQR and XYZ are similar by AA Similarity Theorem

so

[tex]\frac{XY}{PQ}=\frac{YZ}{QR}=\frac{XZ}{PR}[/tex]

Let

z ---> the scale factor

[tex]z=\frac{XY}{PQ}[/tex]

substitute the given values

[tex]z=\frac{30}{5}=6[/tex]

step 2

Find the perimeter of triangle XYZ

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z ----> the scale factor

p_1 ----> the perimeter of triangle XYZ

p_2 ---> the perimeter of triangle PQR

so

[tex]z=\frac{p_1}{p_2}[/tex]

The perimeter of triangle PQR is

[tex]p_2=5+10+6=21\ cm[/tex]

we have

[tex]z=6\\p_2=21\ cm[/tex]

substitute

[tex]6=\frac{p_1}{21}[/tex]

[tex]p_1=6(21)=126\ cm[/tex]

therefore

The perimeter of triangle XYZ is 126 cm

akposevictor akposevictor · Answer 2 · 2022-04-08T09:41:39+02:00

The Perimeter of ΔXYZ that is similar to ΔPQR is: 126 cm.

What are Similar Figures?

The corresponding side lengths of similar figures are proportional, that is, their ratios are equal.

Given that ΔPQR and ΔXYZ are similar, we would have the following ratios:

PQ/XY = PR/XZ = QR/YZ

PQ = 5 cm
PR = 6 cm
QR = 10 cm
XY = 30 cm

Find XZ and YZ using their ratios:

PQ/XY = PR/XZ

Substitute

5/30 = 6/XZ

XZ = (6 × 30)/5

XZ = 36 cm

5/30 = 10/YZ

YZ = (10 × 30)/5

YZ = 60 cm

Perimeter of ΔXYZ = XY + XZ + YZ

Perimeter of ΔXYZ = 30 + 36 + 60

Perimeter of ΔXYZ = 126 cm.

Learn more about similar figures on:

https://brainly.com/question/4381215