Question

which set of side lengths could be used to form a right triangle? 18 in., 19.5 in., 21.5 in. 7.5 in., 19.5 in., 21.5 in. 7.5 in., 18 in., 21.5 in. 7.5 in., 18 in., 19.5 in.

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Check each set

• Set 1: \(18\), \(19.5\), \(21.5\)

\(18^{2}+19.5^{2}=324 + 380.25=704.25\), \(21.5^{2}=462.25\), \(704.25
eq462.25\)

• Set 2: \(7.5\), \(19.5\), \(21.5\)

\(7.5^{2}+19.5^{2}=56.25+380.25 = 436.5\), \(21.5^{2}=462.25\), \(436.5
eq462.25\)

• Set 3: \(7.5\), \(18\), \(21.5\)

\(7.5^{2}+18^{2}=56.25 + 324=380.25\), \(21.5^{2}=462.25\), \(380.25
eq462.25\)

• Set 4: \(7.5\), \(18\), \(19.5\)

\(7.5^{2}+18^{2}=56.25+324 = 380.25\), \(19.5^{2}=380.25\)

Answer:

\(7.5\) in., \(18\) in., \(19.5\) in.