How many Pythagorean triples can be created by multiplying the side lenghts in a known triple by a constant? Explain

1 answer:

Rudiy274 years ago

5 0

Answer: There are an infinite amount of Pythagorean Triples that could be created.

A Pythagorean Triple is a set of 3 integers that would form a right triangle. They must satisfy the equation a^2 + b^2 = c^2.

The most basic one is: 3, 4, 5

A triangle with sides of 3, 4, 5 would form a right triangle.

If we multiply each side by 2, we get 6, 8, 10. This would also be a right triangle.

We could also multiply by 3, or 4, or 5, or 6 .......

We can multiply by any number and still have a right triangle.

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Big Brothers, Inc. borrows $267,999 from the bank at 18.16 percent per year, compounded annually, to purchase new machinery. Thi

Katyanochek1 [597]

Based on the amount borrowed and the interest per year, Big Brothers, Inc will pay an annual payment of $59,973.15.

<h3>How much will Big Brothers, Inc. pay annually?</h3>

This can be found by using the present value of an annuity formula because the annual payment will be constant and therefore like an annuity.

Formula is:

Present value of annuity = Annual payment x ( 1 - (1 + rate) ^ -number of periods) / rate

Solving gives:

267,999 = Amount x ( 1 - ( 1 + 18.16%)⁻¹⁰) / 18.16%

267,999 = Amount x 4.46865

Amount = 267,999 / 4.46865