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A right triangle has legs of length ft and ft. Which is the length of the hypotenuse of the triangle?
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0. Review of College Algebra
Pythagorean Theorem & Basics of Triangles
Multiple Choice
Given three positive numbers, how can you determine if they form a Pythagorean triple?
A
Check if all three numbers are consecutive integers.
B
Check if the product of the two smaller numbers equals the largest number.
C
Check if the sum of the two smaller numbers equals the largest number.
D
Check if the sum of the squares of the two smaller numbers equals the square of the largest number, that is, if .
검증된 단계별 안내1
Identify the three positive numbers and label them as \(a\), \(b\), and \(c\), where \(c\) is the largest number.
Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) equals the sum of the squares of the other two sides.
To check if the numbers form a Pythagorean triple, calculate the squares of the two smaller numbers: \(a^2\) and \(b^2\).
Calculate the square of the largest number: \(c^2\).
Compare the sum of the squares of the two smaller numbers to the square of the largest number by verifying if \(a^2 + b^2 = c^2\). If this equality holds true, the numbers form a Pythagorean triple.
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