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weqwewe [10]
3 years ago
11

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
Mathematics
1 answer:
maw [93]3 years ago
5 0

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.

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