Question

1. which of the following sets of numbers can form a right triangle?

a. 6,8,10
b. 2,3,4
c. 5,7,9
d. 3,4,6

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.

Step2: Check option a

For \(a = 6\), \(b = 8\), \(c = 10\).
\(a^{2}=6^{2}=36\), \(b^{2}=8^{2}=64\), \(c^{2}=10^{2}=100\).
\(a^{2}+b^{2}=36 + 64=100=c^{2}\).

Step3: Check option b

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

Step4: Check option c

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

Step5: Check option d

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

Answer:

A. 6, 8, 10