Question

ΔRST and ΔXYZ are equilateral triangles. The ratio of the perimeter of ΔRST to the perimeter of ΔXYZ is 1 to 3. The area of ΔRST is 10.825 square inches. What is the area of ΔXYZ? (round to nearest tenth)

Answer 1

Answer: D- 97.4

Step-by-step explanation:

For the scale factor of 1:3. Use ratio and proportion to solve for the area of the triangle. 

area of triangle RST/ area of triangle XYZ = (1/3)^2

where

area of traianlge RST = 10.825 inch^2

Area of triangle XYZ= Area of triangle RST x (3)^2

Substitute the given values=97.4 inch^2

Answer 2

Answer:

≈ 97.4 in²

Step-by-step explanation:

Given that the ratio of the perimeter = a : b

then ratio of areas = a² : b²

The ratio of perimeter = 1 : 3 , thus

ratio of area = 1² : 3² = 1 : 9

The area of Δ XYZ is therefore 9 times the area of Δ RST

area of Δ XYZ = 9 × 10.825 = 97.425 ≈ 97.4 ( to the nearest tenth )