Question

If RX=4 and XS=9, then XT=
And how do you get it?

Answer 1

XT=6 units

Explanation:

The picture of the question is the attached figure

step 1

In the right triangle RST

Applying the Pythagorean theorem

`RS^2=RT^2+TS^2`

we have

`RS=RX+XS=4+9=13\ units` ---> by segment addition postulate

substitute

`RT^2+TS^2=169` ----> equation A

step 2

In the right triangle RTX

Applying the Pythagorean theorem

`RT^2=RX^2+XT^2`

we have

`RX=4\ units`

substitute

`RT^2=4^2+XT^2`

`RT^2=16+XT^2`

`XT^2=RT^2-16` ----> equation B

step 3

In the right triangle XTS

Applying the Pythagorean theorem

`TS^2=XS^2+XT^2`

we have

`XS=9\ units`

substitute

`TS^2=9^2+XT^2`

`TS^2=81+XT^2`

`XT^2=TS^2-81` ----> equation C

step 4

equate equation B and equation C

`TS^2-81=RT^2-16`

`TS^2-RT^2=81-16`

`TS^2-RT^2=65` ----> equation D

step 5

Solve the system

`RT^2+TS^2=169` ----> equation A

`TS^2-RT^2=65` ----> equation D

Solve by elimination

Adds equation A and equation D

`RT^2+TS^2=169\\TS^2-RT^2=65\\---------\\TS^2+TS^2=169+65\\2TS^2=234\\TS^2=117`

Find the value of RT^2

`RT^2+117=169\\RT^2=52`

step 6

Find the value of XT

equation C

`XT^2=117-81\\XT^2=36\\XT=6\ units`