To calculate the length of the base of the pyramid, we need to apply the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides (height and half the base length).
Let's denote the height as h = 35 mi, the slant height as s = 37 mi, and the base length as b. We'll also denote r as half the base length.
Using the Pythagorean theorem, we have:
s^2 = h^2 + r^2
Plugging in the given values:
37^2 = 35^2 + r^2
Simplifying:
1369 = 1225 + r^2
Subtract 1225 from both sides:
r^2 = 144
To find the base length (b), we simply double the value of r:
b = 2r
b = 2 * √144
b = 2 * 12
b = 24 mi
To convert the base length from miles to feet, we know that 1 mile is equal to 5280 feet. So to get the length in feet, we multiply the base length in miles by 5280:
base length in feet = 24 mi * 5280 ft/mi
base length in feet = 126,720 ft
Therefore, the base of the pyramid is 24 miles long and 126,720 feet long.
how many miles long is the base of the pyramid? the height is 35mi and the slant is 37mi the base of the square pyramid is how many feet long?
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