A triangle has sides with lengths of 19 millimeters, 26 millimeters, and 30 millimeters. Is it a right triangle?
Question
A triangle has sides with lengths of 19 millimeters, 26 millimeters, and 30 millimeters. Is it a right triangle?
Solution
To determine if a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is often written as a^2 + b^2 = c^2.
In this case, we can consider the longest side, 30 mm, to be the hypotenuse. The other two sides are 19 mm and 26 mm.
First, square the lengths of the two shorter sides and add them together:
19^2 + 26^2 = 361 + 676 = 1037
Then, square the length of the longest side:
30^2 = 900
Since 1037 is not equal to 900, the triangle is not a right triangle according to the Pythagorean theorem.
Similar Questions
A triangle has sides with lengths of 30 centimeters, 35 centimeters, and 45 centimeters. Is it a right triangle?
A triangle has sides with lengths of 15 inches, 18 inches, and 20 inches. Is it a right triangle?
A triangle has sides with lengths of 3 meters, 5 meters, and 6 meters. Is it a right triangle?
A triangle has sides with lengths of 7 feet, 24 feet, and 25 feet. Is it a right triangle?
orWatch a videoA triangle has sides with lengths of 10 inches, 12 inches, and 15 inches. Is it a right triangle?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.