Question

areas of four triangles are 40 cm^2, 90 cm^2, 202.5 cm^2 and 455.6 cm^2 are continue in sequence. the enlargement factor is 1.5, which triangle have first area of 15000 cm^2

Answer 1

Answer:

9th Triangle

Step-by-step explanation:

Given the area of four triangles:$40 cm^2, 90 cm^2, 202.5 cm^2 \:and\: 455.6 cm^2$

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:

$A(n)=40\cdot1.5^{2(n-1)}$

We want to determine which triangle has an area greater than $15000cm^2$.

When A(n)=15000

$40\cdot1.5^{2(n-1)}>15000\\1.5^{2(n-1)}>\frac{15000}{40} \\1.5^{2(n-1)}>375\\\text{Change to Logarithm form}\\2(n-1)>Log_{1.5}375\\\text{Applying logarithm change of base to base 10 law}\\2(n-1)>\frac{Log 375}{Log 1.5} \\2n-2>14.62\\2n>14.62+2=16.62\\n>8.31$

Therefore, the 9th triangle has an area greater than $15000cm^2$.