To solve this problem, we can use the Pythagorean theorem. Let's label the unknown leg of the right triangle as "x". We know that one leg is x, the other leg is the base of the square pyramid, and the hypotenuse is the slant height of the pyramid.
According to the Pythagorean theorem, we have:
x^2 + b^2 = c^2
where x is the length of the unknown leg, b is the length of the base of the square pyramid, and c is the slant height.
Substituting the given values, we get:
x^2 + b^2 = 25^2
x^2 + b^2 = 625
Now, we also know that the height of the pyramid is 20 miles. The height forms a right triangle with the base and the slant height as the hypotenuse. Therefore, we can use the Pythagorean theorem again:
b^2 + 20^2 = c^2
b^2 + 400 = 625
b^2 = 625 - 400
b^2 = 225
Now, we can substitute this value of b^2 back into the first equation:
x^2 + 225 = 625
x^2 = 625 - 225
x^2 = 400
Taking the square root of both sides:
x = sqrt(400)
x = 20
Therefore, the length of the base of the square pyramid is 20 miles.
Look at the square pyramid in the image shown. With the given measurements, determine the length of the base of the square pyramid. A square pyramid with a height of 20 miles, a slant height (diagonal) of 25 miles, and an unknown leg of a right triangle. The question is asking for the base of the square pyramid, not just x!
a2+b2=c2
(10 points)
The base length of the square pyramid is
miles long
1 answer
1 answer