An egyptian pyramid has a square base that measures 80 meters on each side. if the height of the pyramid is 30 meters, what is the slant height of the pyramid?

50 meters

The slant height is the height of a triangle making up the base of the pyramid. We can imagine a right triangle with one leg being a vertical line from the peak of the pyramid going down to the center of the base, and the other leg going from the center of the base to the center of one edge of the base. And finally, the hypotenuse will join the ends of those 2 lines together and will also be the slant height of the pyramid. Then we can easily use the Pythagorean theorem to determine the slant height. So
S = sqrt((80/2)^2 + 30^2)
S = sqrt(40^2 + 30^2)
S = sqrt(1600 + 900)
S = sqrt(2500)
S = 50

So the slant height of the specified pyramid is 50 meters.