Question
A triangle with sides of lengths 9,22 , and 24 is a right triangle.
A. True
B. False
A. True
B. False
Ask by Chang Wood. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The triangle is not a right triangle, so the answer is B. False.
Solution
To determine if a triangle with sides of lengths 9, 22, and 24 is a right triangle, we can use the Pythagorean theorem. According to the theorem, a triangle is a right triangle if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides.
Let’s identify the sides:
- The longest side is 24.
- The other two sides are 9 and 22.
Now, we will check if the following equation holds:
where
Calculating:
Now, let’s perform the calculations.
Now, we will check if
Now we compare:
Since
Thus, the answer is:
B. False
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Simplify this solution Mind Expander
To determine whether the triangle with sides of lengths 9, 22, and 24 is a right triangle, we can apply the Pythagorean theorem, which states that for a triangle to be right-angled, the square of the length of the longest side should equal the sum of the squares of the other two sides. Here, 24 is the longest side. We calculate:
24² = 576, and 9² + 22² = 81 + 484 = 565. Since 576 is not equal to 565, the statement is false.
So, the answer is B. False.
Additionally, it’s essential to remember that right triangles are not just about satisfying the Pythagorean theorem. They can also be identified in real-world scenarios, like in construction or navigation, where having the right angle can help ensure structures are square or help in determining the shortest path.
Fun fact: The concept of right triangles dates back to ancient civilizations! The Egyptians and Babylonians used simple geometric principles that involved right triangles for building pyramids and laying out their cities as far back as 3000 BC.
