First draw F between E and G in a line.
FG = EG - EF
FG = 4x - 3 - x - 7
FG = 3x - 4
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>
Ted:
4,000 @ 4.5% interest compounded annually
Alan:
1,000 @ 6% interest compounded annually
Rule of 72: divide 72 by the compound annual interest rate
Ted: 72/4.5% = 16 years
Alan: 72/6% = 12 years
<span>Alan will win. It will take 12 years.</span>
