The triangle contains two right triangles. The base of each right triangle is equal. Given that the length of the base of the triangle is 10, the base of each right triangle is
10/2 = 5
The diagram of the right triangle is shown below
We would find x by appying the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the diagram,
hypotenuse = 13
one leg = 5
other leg = x
By applying the pythagorean theorem,
13^2 = 5^2 + x^2
169 = 25 + x^2
Subtracting 25 from both sides of the equation, we have
169 - 25 = 25 - 25 + x^2
x^2 = 144
x = square root of 144
x = 12
