Select three ratios that are equivalent to 8 : 5
2 answers:
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Answer:
The answer is below
Step-by-step explanation:
a) Triangle A is attached in the image below.
The base of triangle A is 3 units and its height is 3 units. The area of a triangle is given as:
Area = (1/2) × base × height
Area of triangle A = (1/2) × base × height = (1/2) × 3 × 3 = 4.5 unit²
Area of the scaled copy = 72 unit²
Ratio of area = Area of the scaled copy / Area of triangle A = 72 unit² / 4.5 unit² = 16
Hence the scaled copy area is 16 times larger than that of triangle A.
b) For the scaled copy:
Area of the scaled copy = (1/2) × base × height = 72 unit²
base × height = 144
Since the base and height are equal
base² = 144
base = 12, also height = 12
Base of scaled copy = 12 = 4 × base of triangle A
Therefore the scale factor used is 4
The rows add up to
The sum of the numbers in row
The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When
so the base case holds. Assume the claim holds for
Use this to show that it holds for
Notice that
So you can write the expansion for
and since
and so the claim holds for
Setting
which agrees with the result obtained for part (c).