Question

PLEASE HELP!
The Great Pyramid of Khufu is an architectural masterpiece. It was built from 2,000,000 blocks. The faces are in the shape isosceles triangles. A smaller nearby pyramid is geometrically similar to the Great Pyramid of Khufu, as shown below.

What proportion can be used to find the length, x, of the base of the smaller pyramid?

Answer 1

Corresponding parts of similar triangles are proportional (CPSTP) is the property used here. Since the triangles are isosceles, then each non-base side is the same. The larger/left triangle has both sides of 215 meters and the smaller/right triangle has both sides of 43.

Let's make a proportion. On the tops are the sides, on the bottoms are the bases. On the left is the larger triangle, on the right is the smaller triangle. Keeping the pieces straight is what makes the proportion work.

$\frac{215}{230} = \frac{43}{x}$

To solve for x we can cross multiply.

215(x) = (230)(43)

215x = 9890

x = 46 after dividing both sides by 215

Thus the proportion is $\frac{215}{230} = \frac{43}{x}$ and the base is 46 meters.