Question

Please help: 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: A

Step-by-step explanation: 97.4 in2

A =

3

4

s2

s2 =

4A

3

s2 =

4(10.825)

3

s2 = 25

s = 5

then,

1

3

=

5

x

x = 15

thus, side lengths of ΔXYZ is 15.

A =

3

4

152

A = 97.428

Answer 2

With the given triangles ΔRST and ΔXYZ, it is equilateral triangles and the ratio of the perimeter is 1:3
Perimeter ΔRST/ Perimeter ΔXYZ = 1/3

We are asked to solve for the area of ΔXYZ when the area of ΔRST is 10.825 in². The solution is shown below:
Area ΔRST/ Area ΔXYZ = 1/3
10.825 / Area ΔXYZ = 1/3
Area ΔXYZ = 3* 10.825
Area ΔXYZ= 32.475 in²