Question

The distance between city A and city B is 22 miles. The distance between city B and city C is 54 miles. The distance between city A and city C is 51 miles.
What type of triangle is created by the three cities?

an acute triangle, because 222 + 542 >512
an acute triangle, because 222 + 512 >542
an obtuse triangle, because 222 + 542 >512
an obtuse triangle, because 222 + 512 >542

Answer 1

54 is the hypotenuse because it is the longest side. Square all of the sides. So 54^2=2916
51^2=2601
22^2=484
Now you have 2916=2601+484
Add the two and they will be greater than 2916. Because of that, you will have an acute triangle because 22^2+51^2>54^2
In short, its B

Answer 2

The answer is an acute triangle, because 22^2 + 51^2 > 54^2. In order to find out whether a triangle is acute or obtuse, we must square the lengths of all sides of the triangle. If the largest side's square is less than the two smallest sides' squares added together, than you have an acute triangle. If the largest side's square is larger though, than you have an obtuse triangle.