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What is the length of side TS?

2 is the square root of 6 units
6 is the square root of 6 units
24 units
8 units

What is the length of side TS? 2 is the square root of 6 units 6 is the square root-example-1

1 Answer

2 votes
we know that

in the triangle TQS
applying the Pythagorean theorem
QS²=TS²+TQ²---------> TQ²=QS²-TS²--------> TQ²=18²-9x²-----> equation 1

in the triangle TRS
TS²=TR²+RS²--------------> TR²=TS²-RS²-------> TR²=9x²-144----> equation 2

in the triangle QTR
TQ²=TR²+36-----------> equation 3


I substitute 1 and 2 in 3
18²-9x²=9x²-144+36--------> 18x²-432=0------> x²=24-------> x=√24
x=2√6
TS=3*x------> 3*2√6-----> 6√6
TS=6√6 units

the answer is
TS=6√6 units
6 is the square root of 6 units
User Sleepyjames
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