Question

What is the solution?

Answer 1

If you're looking for c, then the answer is 6 in. I found this answer by using a2+b2=c2 So 4 squared + 5 squared = 41. So then i found the square root of 41 which is 6.40, which rounds to 6.

Answer 2

To find the hypotenuse (the side opposite the right angle) of this right triangle, we turn to one of the oldest and most renowned results in all of mathematics: the Pythagorean Theorem. The Pythagorean Theorem states that the square of the legs of a right triangle is always equal to the square of its hypotenuse (leg²+leg²=hypotenuse²). Here, our legs our 4 and 5 respectively, and our hypotenuse is unknown. Let's call our hypotenuse c. We have:

$4^2+5^2=c^2$

4² = 16, and 5² = 25, so putting the two together, we get:

$16+25=c^2\\41=c^2\\\sqrt{41}=c$

41 is prime, so we cannot reduce this radical any further. The measure of our hypotenuse c is √41.

For reference, and for its sheer elegance, I've included a copy of my favorite proof of the Pythagorean Theorem so you can get a feel for why it works.