A pair of square pyramids are similar. Pyramid A has a base side of 125 inches and a slant height of 160 inches. And pyramid B has a base side of 𝑥 inches and a slant height of 32 inches. Determine the value of 𝑥.
Picking out the key information from the question, we can see that A has a base side of 125 and a slant height of 160. B has a base side of 𝑥 and a slant height of 32. As the two pyramids are similar, one is an enlargement of the other. In this case, pyramid A is an enlargement of pyramid B.
We need to work out the scale factor of the enlargement. As the slant height of pyramid A is 160 inches and the slant height of pyramid B is 32 inches, the scale factor can be calculated by dividing 160 by 32. This gives us an answer of five.
Pyramid A is five times as big as pyramid B. This means that, in order to work out the base side of pyramid B, in this case 𝑥, we can divide 125 by the scale factor five. 125 divided by five is equal to 25. This means that the base side of pyramid B is 25 inches.