Question

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

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

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Calculate hypotenuse for option a

\(a = 7,b = 29\), \(c=\sqrt{7^{2}+29^{2}}=\sqrt{49 + 841}=\sqrt{890}\approx29.83\)

Step3: Calculate hypotenuse for option b

\(a = 15,b = 17\), \(c=\sqrt{15^{2}+17^{2}}=\sqrt{225+289}=\sqrt{514}\approx22.67\)

Step4: Calculate hypotenuse for option c

\(a = 12,b = 13\), \(c=\sqrt{12^{2}+13^{2}}=\sqrt{144 + 169}=\sqrt{313}\approx17.69\)

Step5: Calculate hypotenuse for option d

\(a = 17,b = 18\), \(c=\sqrt{17^{2}+18^{2}}=\sqrt{289+324}=\sqrt{613}\approx24.76\)

Since \(17.69<20\), the right - triangle with \(a = 12,b = 13\) has a hypotenuse less than \(20\)

Answer:

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