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

1 Answer

6 votes

Answer:

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

If RX=4 and XS=9, then XT= And how do you get it?-example-1
User Moia
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