Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To determine whether a triangle with side lengths 2 inches, 5 inches, and 4 inches is acute, we need to apply the properties of an acute triangle.
An acute triangle is defined as a triangle where all three interior angles are less than 90 degrees. One key property of acute triangles is that for each pair of sides, the sum of the squares of the shorter sides must be greater than the square of the longest side.
Let's denote the side lengths as:
- [tex]\(a = 2\)[/tex] inches
- [tex]\(b = 5\)[/tex] inches
- [tex]\(c = 4\)[/tex] inches
First, let's identify the longest side, which is [tex]\(b = 5\)[/tex] inches.
Next, we check if the square of the longest side is less than the sum of the squares of the other two sides:
- Calculate [tex]\(a^2\)[/tex]: [tex]\(2^2 = 4\)[/tex]
- Calculate [tex]\(c^2\)[/tex]: [tex]\(4^2 = 16\)[/tex]
- Calculate [tex]\(b^2\)[/tex]: [tex]\(5^2 = 25\)[/tex]
Now compare:
- [tex]\(a^2 + c^2 = 4 + 16 = 20\)[/tex]
- [tex]\(b^2 = 25\)[/tex]
Since [tex]\(a^2 + c^2 < b^2 \)[/tex] (i.e., [tex]\( 20 < 25\)[/tex]), the condition for the triangle to be acute is not satisfied.
Therefore, the triangle is not an acute triangle. The appropriate explanation is:
"The triangle is not acute because [tex]\(2^2 + 4^2 < 5^2\)[/tex]."
This means that the correct option is:
The triangle is not acute because [tex]\(2^2 + 4^2 < 5^2\)[/tex].
An acute triangle is defined as a triangle where all three interior angles are less than 90 degrees. One key property of acute triangles is that for each pair of sides, the sum of the squares of the shorter sides must be greater than the square of the longest side.
Let's denote the side lengths as:
- [tex]\(a = 2\)[/tex] inches
- [tex]\(b = 5\)[/tex] inches
- [tex]\(c = 4\)[/tex] inches
First, let's identify the longest side, which is [tex]\(b = 5\)[/tex] inches.
Next, we check if the square of the longest side is less than the sum of the squares of the other two sides:
- Calculate [tex]\(a^2\)[/tex]: [tex]\(2^2 = 4\)[/tex]
- Calculate [tex]\(c^2\)[/tex]: [tex]\(4^2 = 16\)[/tex]
- Calculate [tex]\(b^2\)[/tex]: [tex]\(5^2 = 25\)[/tex]
Now compare:
- [tex]\(a^2 + c^2 = 4 + 16 = 20\)[/tex]
- [tex]\(b^2 = 25\)[/tex]
Since [tex]\(a^2 + c^2 < b^2 \)[/tex] (i.e., [tex]\( 20 < 25\)[/tex]), the condition for the triangle to be acute is not satisfied.
Therefore, the triangle is not an acute triangle. The appropriate explanation is:
"The triangle is not acute because [tex]\(2^2 + 4^2 < 5^2\)[/tex]."
This means that the correct option is:
The triangle is not acute because [tex]\(2^2 + 4^2 < 5^2\)[/tex].
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.