Question

two dimensions of a right triangle are 5 units and 13 units. a student writes the equation (5^{2}+13^{2}=c^{2}) to find the length of the third side. answer parts a and b.
a. if all the side lengths are integers, is this student’s equation correct? explain.
a. yes, (5^{2}+13^{2}=25 + 169 = 194). (sqrt{194}) is 14, which is an integer.
b. yes, (5^{2}+13^{2}=25 + 169 = 194). (sqrt{194}) is 18, which is an integer.
c. no, (5^{2}+13^{2}=25 + 169 = 194). (sqrt{194}) is about 13.9, which is not an integer.
d. no, (5^{2}+13^{2}=25 + 169 = 194). (sqrt{194}) is 14.3, which is not an integer.
b. if the student is incorrect, write an equation that will give the length of the third side, and show that the equation is correct. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
a. the student is incorrect. the correct equation is (13^{2}+a^{2}=5^{2}), (a^{2}=square), (a=square)
b. the student is incorrect. the correct equation is (5^{2}+b^{2}=13^{2}), (b^{2}=square), (b=square)
c. the student is correct

Explanation:

Answer:

D. No. $5^2 + 13^2 = 25 + 169 = 194$. $\sqrt{194}$ is about 13.9, which is not an integer.
B. The student is incorrect. The correct equation is $5^2 + b^2 = 13^2$, $b^2 = 144$, $b = 12$