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4 votes
If e = 9 cm and f = 40 cm, what is the length of g?

A. 43 cm
B. 39 cm
C. 31 cm
D. 41 cm

If e = 9 cm and f = 40 cm, what is the length of g? A. 43 cm B. 39 cm C. 31 cm D. 41 cm-example-1

2 Answers

4 votes

Answer:

The answer is D

Explanation:

g= 41 cm

User Walkiria
by
4.6k points
4 votes

(9,40,41) is a Pythagorean Triple, farther down the list than teachers usually venture.

Answer: D. 41 cm

There's a subset of Pythagorean Triples where the long leg is one less than the hypotenuse,

a^2+b^2 = (b+1)^2

a^2 + b^2 = b^2 + 2b +1

a^2=2b+1

So we get one for every odd number, since the square of an odd number is odd and the square of an even number is even.

b = (a^2 - 1)/2

a=3, b=(3^2-1)/2=4, c=b+1=5

a=5, b=(5^2-1)/2 =12, c = 13

a=7, b=24, c=25

a=9, b=40, c=41

a=11, b=60, c=61

a=13, b=84, c=85

It's good to be able to recognize Pythagorean Triples when we see them.

Otherwise we'd have to work the calculator:

√(9² + 40²) = √1681 = 41

User Acg
by
5.8k points
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