Dear Mike,

Can you please do #16 in the Official Practice Test #4 NO CALCULATOR section
(aka Section 3)?

You bet!

This is a question about similar triangles. Here’s a simplified figure we can use to work through it.

Note that I’ve taken the step of drawing a vertical line from the top vertex to the base. Because the shelves are parallel, we know the angles they form with the vertical segment I drew and with the sides of the triangle will all be the same. That tells us that we have angle-angle similarity, so we know that the 2:3:1 ratio we have on the left side will also apply down the middle, like so:

Since we know that the height of the unit is 18 inches, we can solve for y:

y + 3y + 2y = 18
6y = 18
y = 3

From there, we know that the shampoo needs to fit on the middle shelf, so it needs to fit into a space that’s 3y = 3(3) = 9 inches tall.

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