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vagabundo [1.1K]
2 years ago
15

What is the length of side TS?

Mathematics
2 answers:
Jlenok [28]2 years ago
5 0

Answer:

B) 6 Squareroot 6  units

Step-by-step explanation:

balandron [24]2 years ago
3 0

Step-by-step explanation:

In order to find the length of side TS, first we need to find the length of side TR which is perpendicular to side QS.

By Geometric mean property:

{TR}  =  \sqrt{6 \times 12}  \\  \therefore \:  {TR}  =  \sqrt{6 \times 6 \times 2}   \\ \therefore \:  {TR}  =  6\sqrt{2}   \\  \\ In \:  right \:  \triangle  \: TRS:  \\ TS^2 = TR^2 + RS^2  \\ \therefore \:  (3x)^{2}  =  {(6 \sqrt{2}) }^{2}  +  {(12)}^{2}  \\  \therefore \:  9x^{2}  =  72 +  144 \\  \therefore \:  9x^{2}  =2 1 6 \\ \therefore \:  x^{2}  = \frac{2 1 6}{9}  \\ \therefore \:  x^{2}  =24 \\ \therefore \: x =  \sqrt{24}  \\  \therefore \: x = 4.89897949 \\ \therefore \: x  \approx \: 4.9 \\ \therefore \: 3x  = 3 \times 4.9 \\ \therefore \: 3x  =14.7 \\    \huge \red{ \boxed{\therefore  \: TS = 14.7 \: units}}

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