Question

(Pythagorean Theorem MC)

Determine which set of side measurements could be used to form a right triangle.

6, 4, 8
4, 13, 15
16, 8, 18
6, 8, 10

Answer 1

Answer:

$6, 8, 10$

Step-by-step explanation:

To determine which set of side measurements could be used to form a right triangle, we can apply the Pythagorean Theorem.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse ($c$) is equal to the sum of the squares of the lengths of the other two sides ($a$ and $b$):

$c^2 = a^2 + b^2$

Let's check each set of side measurements:

1. $6, 4, 8$:

$8^2 = 6^2 + 4^2$

$64 = 36 + 16$

$64 = 52$

This is not true, so $6, 4, 8$ could not form a right triangle.

2. $4, 13, 15$:

$15^2 = 4^2 + 13^2$

$225 = 16 + 169$

$225 = 185$

This is not true, so $4, 13, 15$ could not form a right triangle.

3. $16, 8, 18$:

$18^2 = 16^2 + 8^2$

$324 = 256 + 64$

$324 = 320$

This is not true, so $16, 8, 18$ could not form a right triangle.

$10^2 = 6^2 + 8^2$

$100 = 36 + 64$

$100 =100$

This is true, so $6, 8, 10$ could form a right triangle.

Therefore, the sets of side measurements could be used to form right triangles:

$6, 8, 10$

Answer 2

Answer:

6, 8, 10

Step-by-step explanation:

A Pythagorean triple is a set of three positive integers, a, b, and c, such that they satisfy the Pythagorean Theorem.

$\boxed{\begin{array}{l}\underline{\sf Pythagorean\;Theorem} \\\\\Large\text{ a^2+b^2=c^2 }\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{ a and b are the legs of the right triangle.}\\\phantom{ww}\bullet\;\textsf{ c is the hypotenuse (longest side) of the right triangle.}\\\end{array}}$

To determine if a set of three integers forms a Pythagorean triple, we can substitute their values into the formula and see if the two sides of the equation match. Remember that the value of c is the largest integer in each case.

Substitute 6, 4, and 8 into the formula:

$\begin{aligned}6^2+4^2&\overset{?}=8^2\\\\36+16&\overset{?}=64\\\\52&\neq64\end{aligned}$

Therefore, 6, 4 and 8 is not a Pythagorean triple as the sum of the squares of the shorter sides does not equal the square of the longest side.

Substitute 4, 13 and 15 into the formula:

$\begin{aligned}4^2+13^2&\overset{?}=15^2\\\\16+169&\overset{?}=225\\\\185&\neq 225\end{aligned}$

Therefore, 4, 13 and 15 is not a Pythagorean triple as the sum of the squares of the shorter sides does not equal the square of the longest side.

Substitute 16, 8 and 18 into the formula:

$\begin{aligned}16^2+8^2&\overset{?}=18^2\\\\256+64&\overset{?}=324\\\\320&\neq 324\end{aligned}$

Therefore, 16, 8 and 18 is not a Pythagorean triple as the sum of the squares of the shorter sides does not equal the square of the longest side.

Substitute 6, 8 and 10 into the formula:

$\begin{aligned}6^2+8^2&\overset{?}=10^2\\\\36+64&\overset{?}=100\\\\100&=100\end{aligned}$

Therefore, 6, 8 and 10 is a Pythagorean triple as the sum of the squares of the shorter sides is equal to the square of the longest side.