SOLUTION: Okay i have no idea how to do this: Given: RECT is a rectangle. RA = 43x AC = 214x-742 Find: The length of ET to the nearest tenth they have a picture o

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Question 122572This question is from textbook Geometry
: Okay i have no idea how to do this:
Given: RECT is a rectangle.
RA = 43x
AC = 214x-742
Find: The length of ET to the nearest tenth
they have a picture of the rectangle but i dont know how to put it on here.
This question is from textbook Geometry

Found 2 solutions by checkley71, solver91311:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
YOU HAVE RECT AS THE SIDES OF TYHE RECTANGLE. BUT YOU HAVE AN A IN THE MEASUREMENTS.
WHAT'S WHAT?????

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Discussion



I'm going to presume that you mean RE=43x and EC+=+214x+-742
and that the figure looks something like:



Don't worry about the orientation of the figure (tall-thin vs. short-fat)
because that will all sort itself out when we solve the problem.
Conceptually, this is a relatively straight-forward Pythagorean Theorem problem.
The only difficulty will be the arithmetic because these numbers are truly
ugly. Either your instructor or the author of your book has a mean streak.
Also, you won't be able to determine a fixed value for ET because both of the
rectangle's sides are given in terms of x. The best you will be able to do
is present an expression for ET in terms of x.





Solution



The segment ET makes the hypotenuse of a right triangle and either the segments
RE and RT or CT and EC are the legs. But since this is a rectangle, RE = CT
and RT = EC. So to apply Pythagoras' Theorem, we can say that a = RE and
b = EC. And finally, we can say that ET = c
c%5E2+=a%5E2%2Bb%5E2

c%5E2=%2843x%29%5E2%2B%28214x-742%29%5E2

Square the 'a' term, apply FOIL to the b expression, and gather terms:
c%5E2=1849x%5E2%2B45796x%5E2-158788x%2B550564

c%5E2=47645x%5E2-158788x%2B550564

c=sqrt%2847645x%5E2-158788x%2B550564%29

If you have more information so that x can be determined, you can calculate
the value of that ugliness.