Question

If the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse?

Answer 1

Answer:

$4\sqrt{5}$

Step-by-step explanation:

In order to solve this problem, we can use the pythagorean theorem, which is

a^2 + b^2 = c^2, where and b are the legs of a right triangle and c is the hypotenuse. Since we are given the leg lengths, we can substitute them in. So, where a is we can put in a 4 and where b is we can put in an 8:

a^2 + b^2 = c^2

(4)^2 + (8)^2 = c^2

Now, we can simplify and solve for c:

16 + 64 = c^2

80 = c^2

c = $\sqrt{80}$

Our answer is not in simplified radical form because the number under is divisible by a perfect square, 16. We can divide the inside, 80,  by 16, and add a 4 on the outside, as it is the square root of 16:

c = $4\sqrt{5}$

Answer 2

Answer:

hypotenuse =square root of

8^2+4^2

64+16

80

= 8.94