The Pythagorean theorem is a good place to begin as it relates the 3 lengths given...now what do you get when you expand the binomials?
ABCD is rectangle. If AD = x + 1, CD= 2x -3 & AC= x+2, find AC.
MY ATTEMPT:
i used pythagorean theorems:
(x +1)^2+ (2x-3)^2 = (x+2)^2
i got the problem from our textbook ... And the answer without solution is at the back of the portion of the book. It says that the answer is 5.
how did they make it to 5, please let me understand.
thanks
(AD)2 + ( CD)2 = (AC)2
(x+1)2 + ( 2x-3)2 = ( x + 2 )2
x^2 + 2x + 1 + 4x^2 – 12x + 9 = x^2 + 4x + 4
4x^2 -14x + 6 = 0
2x^2 -7x + 3 = 0
2x^2 - x – 6x + 3 = 0
( 2x – 1 ) ( x -3)= 0
X = ½ or x = 3. X cannot be ½ because then CD will become negative, thus discarding this value.
Now x = 3 thus AC = x + 2 = 3+2=5
Good forum etiquette dictates that one not give a solution immediately after someone else has given a suggestion on how to proceed. This devalues the preceding post.
You would have learned more had you expanded the binomials yourself, and realized only 1 of the roots made sense in the context of the problem.