Finding the missing length

Question

How do i find the ST??

What more information do I need?

I used Pythagorean theorem, but I still can't find the answer.

Answer 1

Try solving it this way. The area of the parallelogram can be determined using two different expressions: (1) by taking the total area of the rectangle and subtracting the triangle areas, and (2) by multiplying the height (unknown) and width of the parallelogram. Set the two equal to each other, and then use the Pythagorean theorem to find the length $ST$.

What answer do you get?

Answer 2

Consider the following diagram:

Now, $y^2=25-x^2=162-(13-x)^2$

Solve for $x$.