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lyudmila [28]
3 years ago
6

NEED HELP what is X in the diagram ​

Mathematics
1 answer:
Wewaii [24]3 years ago
4 0

Answer:

x=6\sqrt{3}

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ABC

Applying the Pythagoras Theorem

Find out the length side AB

AC^2=AB^2+BC^2

AB^2=AC^2-BC^2

substitute the given values

AB^2=12^2-x^2

AB^2=144-x^2

step 2

In the right triangle ABD

Applying the Pythagoras Theorem

Find out the length side BD

AB^2=AD^2+BD^2

BD^2=AB^2-AD^2

substitute the given values

BD^2=144-x^2-3^2

BD^2=144-x^2-9

BD^2=135-x^2 -----> equation A

step 3

In the right triangle BCD

Applying the Pythagoras Theorem

Find out the length side BD

BC^2=DC^2+BD^2

BD^2=BC^2-DC^2

substitute the given values

BD^2=x^2-9^2

BD^2=x^2-81 -----> equation B

step 4

equate equation A and equation B

BD^2=135-x^2 -----> equation A

BD^2=x^2-81 -----> equation B

x^2-81=135-x^2

x^2+x^2=135+81

2x^2=216

x^2=108

x=\sqrt{108}

Simplify

x=6\sqrt{3}\ units

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