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 betweeb city A and city C is 51 miles.
What type of trianglr is created by the three cities?

A. An acute triangle, beacuse 22^2+54^2>51^2
B. An acute triangle, beacuse 22^2+51^2>54^2
C. An obtuse triangle, beacuse 22^2+54^2>51^2
D. An obtuse triangle, beacuse 22^2+51^2>54^2,

Answer 1

The answer is B. It is an acute triangle because of 22^2 + 51^2 > 54^2. To identify the type of triangle referred to the problem, we use the Pythagorean Theorem which involves squaring the lengths of all sides of the triangle. If the hypotenuse’s square is less than the two smallest sides' squares added together, than it is an acute triangle. However, if the hypotenuse’s square is larger, then it is an obtuse triangle.

54 is the hypotenuse since it is the longest side.

Following the Pythagorean Theorem, a^2 + b^2 = c^2:

54^2=2916

51^2=2601

22^2=484

It becomes 2601+484 = 2916.

When the two shorter sides are added, the sum is greater than the square of the hypotenuse which is 2916. Thus, the formed triangle is acute.