If RS = 9, ST = 12, and RU = 20, find UT.

Question

In quadrilateral RSTU, RS ⊥ ST and UT ⊥ diagonal RT.

If RS = 9, ST = 12, and RU = 20,

 find UT.

Answer 1

You have to use the Pythagorean Theorem (a² + b² = c²) twice.

Step 1. Use the Pythagorean Theorem to find RT in the triangle RST:

RS² + ST² = RT²

You know the values of RS and ST, so plug them in to find RT.

Step 2. Now that you have RT, use the Pythagorean Theorem again on triangle RTU:

RT² + UT² = RU²

The problem tells you the value of RU and you found the value of RT in step 1. Plug them in and solve for UT.