Select the correct answer from each drop-down menu. The sides of ABC are 30 units, 40 units, and 60 units long. The corresponding sides of AXYZ are r times as long
as the sides of AABC.
2. If the area of AABC is n square units, the
The expression that gives the perimeter of AXYZ is
area of AXYZ is
square units.

The expression that gives the perimeter of ΔXYZ is: 130r

The area of ΔXYZ = nr²

If A and B, with sides a and b respectively, are similar figures, therefore: area of A/area of B = a²/b².

Thus;

Given that the sides of ΔABC, which are 30, 40 and 60, are r times the corresponding sides of ΔXYZ, the sides of XYZ would be:

30r, 40r, 60r.

Perimeter of ΔXYZ = 30r + 40r + 60r = 130r

Given that the area of ΔABC is n units², therefore:

(area of ΔABC)/(area of ΔXYZ) = (side of ΔABC)²/(side of ΔXYZ)²

(n)/(area of ΔXYZ) = (30)²/(30r)²

n/area of ΔXYZ = 1/r²

nr² = area of ΔXYZ

area of ΔXYZ = nr²

Therefore, the expression that gives the perimeter of ΔXYZ is: 130r

The area of ΔXYZ = nr²

Learn more about area of similar figures on:

link

Area of ΔXYZ = n(r * r) square units

Step-by-step explanation:

Sides of ΔABC are 30 units, 40 units and 60 units.

Corresponding sides of another triangle XYZ are r times as long as the sides of ΔABC.

Therefore, sides of ΔXYZ will be, 30r units, 40r units and 60r units.

Perimeter of the triangle XYZ = 30r + 40r + 60r

                                                   = 130r units

If the area of ΔABC = n square units

Then the ratio of the area of ΔXYZ and ΔABC = (Ratio of the sides of ΔXYZ and ΔABC)²

Area of ΔXYZ = nr² ≈ n(r * r)

Therefore, Option (3) will be the answer.