Answer:
[tex]x=7.4[/tex] m and [tex]x=11.2[/tex] m
Step-by-step explanation:
To do these problems, we will need to use the Pythagorean Theorem.
Recall that it states [tex]a^2+b^2=c^2[/tex], where c is the longest side, the hypotenuse, of the triangle.
a) We have a triangle with side lengths 4.2 m and 6.1 m. These two sides correspond to a and b in this equation.
Now, we can plug these values into the equation and solve for c, which is x.
[tex](4.2)^2+(6.1)^2=x^2\\\\17.64+37.21=x^2\\\\x=\sqrt{54.85}\\\\x=7.406\\\\x=7.4[/tex]
b) We have a triangle with side lengths 5.1 m and 12.3 m. These sides correspond to a and c, so b will be x.
Now, we can plug these values into the equation and solve for x.
[tex](5.1)^2+x^2=(12.3)^2\\\\26.01+x^2=151.29\\\\x=\sqrt{151.29-26.01}\\\\x=\sqrt{125.28}\\\\x=11.193\\\\x=11.2[/tex]
