Final Answer:
It is untrue for Estevan to say that these side lengths cannot form a right triangle. So, choice B is the right one.
Step-by-step explanation:
To determine whether a triangle with side lengths of 21 inches, 75 inches, and 72 inches can be a right triangle, we can employ the Pythagorean theorem.
The theorem states that for any 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 can be written as: a^2 + b^2 = c^2
where:
c is the length of the hypotenuse,
a and b are the lengths of the other two sides.
If the given side lengths satisfy this equation, the triangle can be a right triangle.
Taking the given side lengths, we should identify the longest side to be the hypotenuse (c). Here, the longest side is 75 inches. Thus, side1 (a) is 21 inches, and side2 (b) is 72 inches.
Now, let's plug these values into the Pythagorean theorem to test if the triangle is right-angled:
21^2 + 72^2 ?= 75^2
Calculating each term:
21^2 = 21 * 21 = 441
72^2 = 72 * 72 = 5184
75^2 = 75 * 75 = 5625
Now, we add 21^2 and 72^2:
441 + 5184 = 5625
Notice that the sum equals 75^2 (5625). Therefore, the equation holds true:
441 + 5184 = 5625
5625 = 5625
Since the sum of the squares of the two shorter sides equals the square of the longest side, the triangle with sides 21 inches, 75 inches, and 72 inches can indeed be a right triangle.
Therefore, Estevan's claim that a right triangle cannot be made with these side lengths is incorrect.
Answer: b) No, he is incorrect.