Question

calculate the hypotenuse of each right triangle with the given leg lengths. which one has a hypotenuse less than 20? a. ( a = 17, b = 18 ) b. ( a = 15, b = 17 ) c. ( a = 12, b = 13 ) d. ( a = 7, b = 29 )

Explanation:

Step1: Apply Pythagorean theorem for option a

The Pythagorean theorem is \(c = \sqrt{a^{2}+b^{2}}\). For \(a = 17\), \(b = 18\), we have \(c=\sqrt{17^{2}+18^{2}}=\sqrt{289 + 324}=\sqrt{613}\approx24.76\)

Step2: Apply Pythagorean theorem for option b

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

Step3: Apply Pythagorean theorem for option c

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

Step4: Apply Pythagorean theorem for option d

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

Answer:

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