Mrs. Ibarra wants to create a right triangle for a geometry test. She plans to use 15, 36, and 41 as side lengths.
Select the four true statements regarding the side lengths Mrs. Ibarra chose.
15 + 36 greater-than 41, so the side lengths will form a triangle.
15 + 36 not-equals 41, so those lengths will not form a triangle.
15 squared + 36 squared = 1,521
41 squared = 1,681
Since a squared + b squared not-equals c squared, it will not be a right triangle.
15 squared + 36 squared = 297
41 squared = 82
The four true statements regarding the side lengths Mrs. Ibarra chose are:
1. 15 + 36 is greater than 41, so the side lengths will form a triangle.
2. 15 squared + 36 squared = 1,521.
3. 41 squared = 1,681.
4. Since 15 squared + 36 squared does not equal 41 squared, it will not be a right triangle.
Mrs. Ibarra wants to create a right triangle for a geometry test. She plans to use 15, 36, and 41 as side lengths.
Select the four true statements regarding the side lengths Mrs. Ibarra chose.
15 + 36 greater-than 41, so the side lengths will form a triangle.
15 + 36 not-equals 41, so those lengths will not form a triangle.
15 squared + 36 squared = 1,521
41 squared = 1,681
Since a squared + b squared not-equals c squared, it will not be a right triangle.
15 squared + 36 squared = 297
41 squared = 82
The four true statements regarding the side lengths Mrs. Ibarra chose are:
1. 15 + 36 is greater than 41, so the side lengths will form a triangle.
2. 15 squared + 36 squared = 1521.
3. 41 squared = 1681.
4. Since 15 squared + 36 squared does not equal 41 squared, it will not be a right triangle.
Tasha assembled a picture frame that is advertised as rectangular. The completed frame is 14 inches long and 10 inches wide. She measured the diagonal length across the frame as 20 inches. Which best explains why the frame cannot actually be rectangular?
14 squared + 10 squared not-equals 20 squared
14 + 10 not-equals 20
(14 + 10) squared not-equals 20 squared
(14 squared + 10 squared) squared not-equals 20 squared
The best explanation why the frame cannot actually be rectangular is that 14 squared + 10 squared does not equal 20 squared.
Arnob may want to borrow his cousin’s tent, which is shown below.
2 right triangles share a side to form a larger triangle. Each triangle has a side length of 4 feet and hypotenuse of 9 feet. The shared side is x.
He needs to determine x, the center height of the tent, to determine if it will be large enough for his camping trip. What is the center height of this tent, to the nearest tenth of a foot?
4.1 feet
8.1 feet
9.8 feet
12.0 feet
To determine the center height of the tent, we can consider the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, we have two right triangles with a side length of 4 feet and a hypotenuse of 9 feet. We need to find the length of the shared side, which is represented by x.
Using the Pythagorean theorem, we can solve for x:
x^2 + 4^2 = 9^2
x^2 + 16 = 81
x^2 = 65
x ≈ √65 ≈ 8.1 feet
Therefore, the center height of the tent is approximately 8.1 feet.
Which statements are true? Select the five correct answers.
StartRoot 1.8 EndRoot < 1.8
StartRoot 1.8 EndRoot greater-than 1
StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot
1.3 less-than StartRoot 1.8 EndRoot less-than 1.4
StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2
StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
The five correct statements are:
1. StartRoot 1.8 EndRoot < 1.8
2. 1.3 less-than StartRoot 1.8 EndRoot less-than 1.4
3. StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2
4. StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
5. StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot
Nadia says the hypotenuse of this right triangle has a length of 73 because the Pythagorean theorem states that (28 + 45) squared = 73 squared.
3 squares are positioned to form a right triangle. The small square is labeled 28, medium square is 45, and large square is not labeled.
Which best describes Nadia’s solution?
She is correct because she applied the Pythagorean theorem properly and her arithmetic is accurate.
She is incorrect because she should have used 45 as the length of the hypotenuse.
She is incorrect because she should have squared each leg length and then found the sum.
She is correct because the hypotenuse is the longest side of the triangle.