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. NextReset

Answer 1

The perimeter of ABC = a + b + c, where a, b, c are the sides of the triangle. 
The perimeter is 30 + 40 + 60 = 130

The perimeter of XYZ is r*a + r*b + r*c,
Factoring: r (a + b + c) 
We know that a + b + c = 130, so...
Perimeter XYZ = 130r

Area:
The scale factor of the triangles is r
If two similar triangles have a scale factor of r, the ratio of their scale factors is 1:r²
The area of triangle ABC is n²
The area of triangle XYZ is, therefore, r²*n² units
Answer is (r²)(n²) units