Answer:

Step-by-step explanation:
![We\ are\ given:\\TU=SQ\\TP=PQ\\\angle TPU= \angle SPQ [Vertically\ Opposite\ Angles\ Are\ Equal]\\Hence,\\As\ we\ are\ given,\ 2\ sides\ and\ 1\ angle\ of\ each\ triangle\ correspond,\ we\\ could\ use\ the\ SAS\ Congruency Rule.\\But:\\](https://tex.z-dn.net/?f=We%5C%20are%5C%20given%3A%5C%5CTU%3DSQ%5C%5CTP%3DPQ%5C%5C%5Cangle%20TPU%3D%20%5Cangle%20SPQ%20%5BVertically%5C%20Opposite%5C%20Angles%5C%20Are%5C%20Equal%5D%5C%5CHence%2C%5C%5CAs%5C%20we%5C%20are%5C%20given%2C%5C%202%5C%20sides%5C%20and%5C%201%5C%20angle%5C%20of%5C%20each%5C%20triangle%5C%20correspond%2C%5C%20we%5C%5C%20could%5C%20use%5C%20the%5C%20SAS%5C%20Congruency%20Rule.%5C%5CBut%3A%5C%5C)
<em>As SAS Congruency Rule tells us that 'Two triangles are congruent only if two sides and an included angle of one triangle corresponds to two sides and an included angle of the other' .</em>
<em>Here,</em>
<em>As ∠TPU and ∠SPQ are NOT the included angle of ΔTUP and ΔSPQ respectively, the two triangles cannot be proven congruent through SAS Congruency.</em>
<em>Note: We also cannot apply SSA congruency as SSA congruency doesnt exist.</em>
The shorter piece is 3 feet
The longer piece is 9 feet
Given :

We know the identity
We use this property to simplify the left hand side
So 

we know ,
when
then

For 

Add
on both sides

Finally we add 2npi for general solution
So options C and D are correct