Question

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.

Answer 1

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

Answer 2

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 $n*r^{2}\ units^{2}$