As you read the stem, you might wonder what an isosceles trapezoid is. If you’ve never heard the
term before, you still might have been able to extrapolate its meaning from what you know of
isosceles triangles. Isosceles means “having two equal sides.” When applied to a trapezoid, the term
isosceles tells you that the two nonparallel sides—the legs—are equal. In this case, that’s and
. If the total perimeter is 62, and the two marked sides add up to 25 + 7 = 32, then the two
unmarked sides split the difference of 62 − 32 = 30. In other words, = = 15.
There aren’t any special triangles yet. As so often happens, though, you can get some by
constructing altitudes. Drop perpendiculars to points Z and Y, and you make two right triangles. The
length 25 of side then gets split into 9, 7, and 9.
Now you can see that those right triangles are 3-4-5s (times 3) and that the height of the trapezoid is
12 because it is a leg of a 9 − x − 15 right triangle. Now look at the right triangle of which is the
hypotenuse.