Answered

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].



Answer :

GinnyAnswer
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].

Other Questions