Question 7114
You are given one side of the triangle and the hypotenuse. You should also know that the sum of the square of the sides of a right triangle equals the hypotenuse squared.

If the sides of the triangle are a and b and the hypotenuse is h, the equation can  be written:

a^2 + b^2 = h^2.

The problem tells us that one side, let's pick a for now, is 10 cm and the square of the hypotenuse is 221 cm. If we include these facts in the equation, we get,

10^2 + b^2 = 221, or

100 + b^2 = 221

Now, subtract 100 from either side to get

b^2 = 221 - 100 = 121

take the square root of either side to get

b = 11

b is the height of the triangle.