<PRE><B>Question 1166466</B>
PQRS is a rectangle in which PQ=10 and PS=6.
 T is the point on PQ such RST is an isosceles triangle whose equal sides are RS and ST.
 Find RT
:
Draw this out.  We know that St = 10 also from the information given
label the line segment TQ as x
We can find x using the right triangle PST, where
side PS given as 6 and the other side (10-x), ST = 10 the hypotenuse
solve for x using pythag
6^2 + (10-x)^2 = 10^2
36 + 100 - 20x + x^2 = 100
Subtract 100 from both sides and arrange as a simple quadratic equation
x^2 - 20x + 36 = 0
Factors to
(x-2)(x-18) = 0
The reasonable solution
x = 2
:
Use the right triangle TQR, where one leg = 2, one leg = 6
Find RT which is the hypotenuse
RT = {{{sqrt(2^2 + 6^2)}}}
RT = 6.32</PRE>