Question

Triangle ABC is a right triangle. The length of the legs are 3 in and 6 in, how long is the hypotenuse? (Round to the nearest tenth if necessary)

A) 3.3 in
B) 6.7 in
C) 7.9 in
D) 9.0 in

Answer 1

Triangle ABC is a right triangle. The length of the legs are 3 in and 6 in, how long is the hypotenuse? (Round to the nearest tenth if necessary)

When the two legs are given, the hypotenuse is found by using the Pythagorean Theorem, which states that:

$\displaystyle a^{2} +b^{2} =c^{2}$

In the theorem, a and b are the two legs, and c is the hypotenuse. Since you are given the length of the two legs, substitute it into the equation.

$a=3\\b=6$

$3^{2} +6^{2}=c^{2}$

Now, you need to square both 3 and 6. When you square a number, you're basically multiplying the number by itself.

$3^{2} =3 \times 3=9\\6^{2}=6 \times 6=36$

Substitute the numbers into the equation.

$9+36=c^{2}$

Add:

$45=c^{2}$

You're looking for the value of c, not c squared. To remove the square, you need to square root it.

$\displaystyle \sqrt{45}=\sqrt{c^{2} }$

Using a calculator, find the square root of 45.

$\displaystyle \sqrt{45}=\sqrt{c^{2} }\\c \approx 6.7$

The answer to your question is B) 6.7 inches.

Answer 2

Answer: A

Step-by-step explanation:

Use Pythagorean Theorem in order to solve this:

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

(c is the hypotenuse)

So that would be:

$3^{2} + 6^{2} = c^{2}$

If you solve this, you would find that:

$c^{2} = 45$

$c = 3\sqrt{5}$

Answer = B