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The sides of ∆ABC are 30 units, 40 units, and 60 units long. The corresponding sides of ∆XYZ are r times as long as the sides of ∆ABC. The expression that gives the perimeter of ∆XYZ is . If the area of ∆ABC is n square units, the area of ∆XYZ is square units.

Verified Answer :

nobillionaireNobley

The sides of triangle XYZ = 30r units, 40r units, and 60r units
The expression that gives the perimeter of XYZ is 30r + 40r + 60r = 130r


calculista

Part a) Find the expression that gives the perimeter of ∆XYZ

we know that

Perimeter of triangle ABC is equal to

\(P=30+40+60\\ P=130\ units\)

In this problem ∆ABC and ∆XYZ are similar triangles

the scale factor is equal to r

so

\(scale\ factor=r \\ \\ scale\ factor=\frac{perimeter\ triangle\ XYZ}{perimeter\ triangle\ ABC} \\ \\ perimeter\ triangle\ XYZ=perimeter\ triangle\ ABC*scale factor\\ \\ perimeter\ triangle\ XYZ=130*r\)

therefore

the answer Part a) is

The expression that gives the perimeter of ∆XYZ is \(130*r\ units\)

Part b) Find the expression that gives the area of ∆XYZ

we know that

\(Area\ of\ triangle\ ABC=n\ units^{2}\)

\(scale\ factor=r \\ \\ scale\ factor^{2}=\frac{Area\ triangle\ XYZ}{Area\ triangle\ ABC} \\ \\ Area\ triangle\ XYZ=Area\ triangle\ ABC*scale factor^{2}\\ \\ Area\ triangle\ XYZ=n*r^{2}\ units^{2}\)

therefore

the answer Part b) is

The expression that gives the Area of ∆XYZ is \(n*r^{2}\ units^{2}\)

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