Question

Given: AR ⊥ RS , TS ⊥ RS AT=26, RS=24 AR=12 Find: TS

Answer 1

The length of TS will be 22.

Explanation

According to the below diagram, AR and TS are perpendicular on the line RS.

Given that,  AR = 12 , RS = 24 and AT = 26

First we will draw a perpendicular line from point A on the line TS, which intersects TS at point B.

So, $AB= RS = 24$ and $BS= AR= 12$

Now in right angle triangle ABT, using Pythagorean theorem we will get.....

$(AT)^2= (AB)^2 +(BT)^2\\ \\ 26^2= 24^2 + (BT)^2\\ \\ (BT)^2= 26^2-24^2\\ \\ (BT)^2=676-576=100\\ \\ BT= \sqrt{100}=10$

So, the length of TS will be: (BT + BS) = (10 + 12) = 22

Answer 2

Answer:

The length of TS will be 22.