Question

Select the correct answer from each drop-down menu.

Answer 1

Answer:

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

$\frac{\text{Area of triangle XYZ}}{\text{Area of triangle ABC}}=(\frac{\text{Side length of XYZ}}{\text{Side length of triangle ABC}})^2$

$\frac{\text{Area of triangle XYZ}}{n}=(r)^2$

Area of ΔXYZ = nr² ≈ n(r * r)

Therefore, Option (3) will be the answer.