What is the area of this triangle?
(hint - area of triangle = 1/2 * base * height)

A^2 + b^2 = c^2
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 169 - 25 = 144
b^2 = 144
sqrt of 144 = 12
x = 12

A = 1/2bh
A = 1/2(5)(12)
A = 30

First, we need to find the length of the unknown side.

The formula to find the hypotenuse is given by:

c^2 = a^2 + b^2

BUT! Since we need to find the length of the shorter side, we rearrange the formula to:

a^2 = c^2 - b^2

Let the unknown side be x,

x^2 = 13^2 - 5^2
x^2 = 144
Square root both sides to get x,
x = 12

Now that you have x, which is the height of the triangle, you need to use the formula to find the area, given by:

A = 1/2 x b x h

In this case, b = 5, and h = 12. Sub these values into the formula:

A = 1/2 x 5 x 12
   = 30

Hope this helped! Ask me if there's any part of the working you don't understand :)