Question

which of the following sets of numbers can form a right triangle?
a. 5,7,9
b. 3,4,6
c. 2,3,4
d. 6,8,10

Explanation:

Step1: Apply Pythagorean theorem

For a set of numbers \(a,b,c\) (\(c\) is the largest number), check if \(a^{2}+b^{2}=c^{2}\)

Step2: Check option a

\(a = 5\), \(b = 7\), \(c = 9\)
\(a^{2}+b^{2}=5^{2}+7^{2}=25 + 49=74\)
\(c^{2}=9^{2}=81\)
Since \(74
eq81\), option a is wrong.

Step3: Check option b

\(a = 3\), \(b = 4\), \(c = 6\)
\(a^{2}+b^{2}=3^{2}+4^{2}=9 + 16=25\)
\(c^{2}=6^{2}=36\)
Since \(25
eq36\), option b is wrong.

Step4: Check option c

\(a = 2\), \(b = 3\), \(c = 4\)
\(a^{2}+b^{2}=2^{2}+3^{2}=4+9 = 13\)
\(c^{2}=4^{2}=16\)
Since \(13
eq16\), option c is wrong.

Step5: Check option d

\(a = 6\), \(b = 8\), \(c = 10\)
\(a^{2}+b^{2}=6^{2}+8^{2}=36+64 = 100\)
\(c^{2}=10^{2}=100\)
Since \(a^{2}+b^{2}=c^{2}\), option d is correct.

Answer:

d. \(6,8,10\)