Answer:
9th Triangle
Step-by-step explanation:
Given the area of four triangles:[tex]40 cm^2, 90 cm^2, 202.5 cm^2 \:and\: 455.6 cm^2[/tex]
If the Scale factor is 1.5.
This is a geometric sequence and the common ratio is 1.5 X 1.5.
Therefore, the area of any n triangle can be determined using the function:
[tex]A(n)=40\cdot1.5^{2(n-1)}[/tex]
We want to determine which triangle has an area greater than [tex]15000cm^2[/tex].
When A(n)=15000
[tex]40\cdot1.5^{2(n-1)}>15000\\1.5^{2(n-1)}>\frac{15000}{40} \\1.5^{2(n-1)}>375\\\text{Change to Logarithm form}\\2(n-1)>Log_{1.5}375\\\text{Applying logarithm change of base to base 10 law}\\2(n-1)>\frac{Log 375}{Log 1.5} \\2n-2>14.62\\2n>14.62+2=16.62\\n>8.31[/tex]
Therefore, the 9th triangle has an area greater than [tex]15000cm^2[/tex].
