SAT Math 6.3 Geometry and Measurement

The altitude of a triangle always runs perpendicular to its base…

…and we can indeed see that a couple of right angles are formed at the bottom.

Which is dandy news.

Now we have ourselves a pair of right triangles.

We can deduce that the base of each right triangle is 5…

…since the length of each full side of the equilateral triangle is 10…

…and our altitude line bisects it.

Yup…slices it right down the middle…like that poor worm you disposed of in biology.

So…now that we have the length of two sides of our right triangle…

…5 for the base and 10 for the hypotenuse…

…we can apply our buddy Pythagoras and his theorem.

5 squared plus our altitude squared equals 10 squared.

Or… 25 plus our altitude squared equals 100.

So the altitude is going to be the square root of the difference,100 - 25, or 75.

Which simplifies to the square root of 25 times 3…

…or 5 square root of 3 and the answer is C.

Beautiful.