Answered

IDNLearn.com: Your one-stop platform for getting reliable answers to any question. Discover in-depth answers from knowledgeable professionals, providing you with the information you need.

Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle?

A. The triangle is a right triangle because [tex]\(5^2 + 12^2 = 13^2\)[/tex].
B. The triangle is a right triangle because [tex]\(5 + 13 \ \textgreater \ 12\)[/tex].
C. The triangle is not a right triangle because [tex]\(5^2 + 13^2 \ \textgreater \ 12^2\)[/tex].
D. The triangle is not a right triangle because [tex]\(5 + 12 \ \textgreater \ 13\)[/tex].

Sagot :

GinnyAnsweridn
To determine if a triangle with side lengths [tex]\(5\)[/tex] cm, [tex]\(12\)[/tex] cm, and [tex]\(13\)[/tex] cm is a right triangle, we need to verify if it satisfies the Pythagorean Theorem. The Pythagorean Theorem states that for a right triangle with side lengths [tex]\(a\)[/tex], [tex]\(b\)[/tex], and hypotenuse [tex]\(c\)[/tex], the following equation holds true:

[tex]\[ a^2 + b^2 = c^2 \][/tex]

Given the side lengths [tex]\(5\)[/tex] cm, [tex]\(12\)[/tex] cm, and [tex]\(13\)[/tex] cm, we can assume that [tex]\(5\)[/tex] cm and [tex]\(12\)[/tex] cm are the legs ([tex]\(a\)[/tex] and [tex]\(b\)[/tex]), and [tex]\(13\)[/tex] cm is the hypotenuse ([tex]\(c\)[/tex]). We need to check the following:

[tex]\[ 5^2 + 12^2 = 13^2 \][/tex]

First, calculate [tex]\(5^2\)[/tex]:

[tex]\[ 5^2 = 25 \][/tex]

Next, calculate [tex]\(12^2\)[/tex]:

[tex]\[ 12^2 = 144 \][/tex]

Now, sum these squares:

[tex]\[ 25 + 144 = 169 \][/tex]

Then, calculate [tex]\(13^2\)[/tex]:

[tex]\[ 13^2 = 169 \][/tex]

We see that:

[tex]\[ 5^2 + 12^2 = 13^2 = 169 \][/tex]

Since [tex]\(5^2 + 12^2 = 13^2\)[/tex], the given side lengths satisfy the Pythagorean Theorem. Therefore, the triangle is a right triangle.

So, the correct explanation is:

The triangle is a right triangle because [tex]\(5^2 + 12^2 = 13^2\)[/tex].
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.