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Montano1993 [528]
3 years ago
9

What is the length of side TS?

Mathematics
2 answers:
-Dominant- [34]3 years ago
6 0
We know that

 in the triangle TQS
<span>applying the Pythagorean theorem
QS</span>²=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


<span>I substitute 1 and 2 in 3
</span>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 
<span>6 is the square root of 6 units</span>
ololo11 [35]3 years ago
5 0

We are given a triangle TQS.

And in triangle TQS, TR is a perpendicular to QS.

Therefore, in triangle TQS and TRS

<QTS = <TRS  :    Right angles .

<S = <S           : Common angles of triangles TQS and TRS.

Therefore  triangles TQS and TRS are similar.

Note: Similar triangle has sides in proportion.

Therefore,

QS/TS =TS/RS

(6+12)/3x = 3x/12.

18/3x = 3x/12

ON cross multiplication, we get

3x*3x = 18 * 12

9x^2 = 216.

Dividing both sides by 9, we get

\frac{9x^2}{9} =\frac{216}{9}

x^2=24

x=\sqrt{24}

Plugging x=\sqrt{24} in 3x, we get

3x = 3(\sqrt{24}) = 3(2\sqrt{6}) =6\sqrt{6}.

<h3>Therefore, the length of side TS is 6\sqrt{6} units.</h3>
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