Question 641963: A rectangle has length of (x+3) m and width of (2x-6) m. It's perimeter is 26 meters. Find the value of x.
I'm not sure how to write this equation! I could solve it once it's written, I'm just not sure of that first step. Thank you in advance!
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! You need to start with the formula for the perimeter, p, of a rectangle, which in term of the lenght, L, and width, W, is
(1) p = 2*L + 2*W or
(2) p = 2*(L + W)
Now substitute the expressions for L = x + 3, and W = 2*x -6, into (2) and obtain
(3) p = 2*(x + 3 + 2x - 6), which simplifies to
(4) p = 2*(3x - 3)
Now use the value of p given for your problem and get
(5) 2*(3x - 3) = 26
Divide both sides by 2 yields
(6) 3x - 3 = 13 or
(7) 3x = 16 and the solution
(8) x = 16/3
Is that the correct value of x? Let's check.
Is (26 = 2*(16/3 + 3 + 2(16/3) - 6))?
Is (26 = 2*(16 + 3 - 6))?
Is (26 = 2*13)?
Is (26=26)? Yes
Answer: x = 16/3
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