1. Use the following set of numbers:
7, 24, 25
Check all that apply below.
The set forms the measures of the sides of a right triangle.
The set forms a Pythagorean triple.
The hypotenuse is 24.
One of the legs of the triangle 25.
The triangle is an acute triangle.
What do you think? I will be happy to check your answers
The set forms the measures of the sides of a right triangle.(true?)
The set forms a Pythagorean triple.(True)
The hypotenuse is 24.(False)
One of the legs of the triangle 25.(false)
The triangle is an acute triangle.
(false)
To determine if the set of numbers forms the measures of the sides of a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem 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.
In this case, we have the numbers 7, 24, and 25. Let's check if the sum of the squares of the two smaller numbers is equal to the square of the largest number:
7^2 + 24^2 = 49 + 576 = 625
25^2 = 625
Since both calculations yield the same result, this means that the set of numbers forms a Pythagorean triple. Therefore, the first statement, "The set forms a Pythagorean triple," is true.
Now let's check the other statements:
- "The set forms the measures of the sides of a right triangle": Since the set forms a Pythagorean triple, this statement is also true.
- "The hypotenuse is 24": The hypotenuse refers to the longest side of a right triangle, which is 25 in this case, so this statement is false.
- "One of the legs of the triangle 25": In this case, 25 is the hypotenuse, not a leg. Therefore, this statement is false.
- "The triangle is an acute triangle": An acute triangle is a triangle where all angles are less than 90 degrees. Given that we have a right triangle (with a right angle), this statement is false.
In summary, the correct statements are:
- The set forms a Pythagorean triple.
- The set forms the measures of the sides of a right triangle.
The incorrect statements are:
- The hypotenuse is 24.
- One of the legs of the triangle is 25.
- The triangle is an acute triangle.