Question

1. calculate the hypotenuse of each right triangle with the given leg lengths. which one has a hypotenuse less than 20?

a ( a = 15, b = 17 )
b ( a = 17, b = 18 )
c ( a = 7, b = 29 )
d ( a = 12, b = 13 )

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\).

For option a:

\(a = 15\), \(b = 17\)
\(c=\sqrt{15^{2}+17^{2}}=\sqrt{225 + 289}=\sqrt{514}\approx22.7\)

For option b:

\(a = 17\), \(b = 18\)
\(c=\sqrt{17^{2}+18^{2}}=\sqrt{289+324}=\sqrt{613}\approx24.8\)

For option c:

\(a = 7\), \(b = 29\)
\(c=\sqrt{7^{2}+29^{2}}=\sqrt{49 + 841}=\sqrt{890}\approx29.8\)

For option d:

\(a = 12\), \(b = 13\)
\(c=\sqrt{12^{2}+13^{2}}=\sqrt{144+169}=\sqrt{313}\approx17.7\)

Answer:

d. \(a = 12,b = 13\)