Question

Triangle Q T S is shown. Angle A T S is a right angle. An altitude is drawn from point T to point R on side Q S to form a right angle. The length of T S is 3 x, the length of Q R is 6, and the length of R S is 12.

What is the length of side TS?

2 StartRoot 6 EndRoot units
6 StartRoot 6 EndRoot units
24 units
8 units

Answer 1

6sqrt6 = 14.69 sqrt14,69 = 3.83

closest divider to 4.12 as <4.5 TS <3.5

Explanation:

RS can be formed as a square so that = 12 can be used for other sides of that square to find the diagonal

Where diagonal square = TS side

12^2 x 12^2 = sqrt 144 + sq rt 144 = TS^2

TS^2 = sq rt 288 = 16.9705627 = 17

We then look at the choice answers 1, 2, 3, 4

sq rt 16.97 = 4.12310563 sq rt 17 = 4.11 where

2 sqrt 6 = 4.898989 so is incorrect.

Answer 2

B. 6
`√(6)`

Explanation:

Edge 2021