SOLUTION: Could you please help me solve this... The sides of a rectangle are A: 5X, B:5Y, C:7Y+7, D: 2X+6 What are the values of the variables and the length of the sides.

Question 551992: Could you please help me solve this...
The sides of a rectangle are A: 5X, B:5Y, C:7Y+7, D: 2X+6
What are the values of the variables and the length of the sides.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your rectangle is:
ABCD
side AB is equal to 5x.
side BC is equal to 5y.
side CD is equal to 7y+7
side AD is equal to 2x+6
side AB is opposite side CD.
side BC is opposite side AD
opposite sides of a rectangle are equal.
this means that:
5x = 7y+7
5y = 2x+6
solve for y in each equation to get:
y = (5x-7)/7 (first equation)
y = (2x+6)/5 (second equation)
since they are both equal to y, then they are both equal to each other and we get:
(5x-7)/7 = (2x+6)/5
multiply both sides of this equation by 35 to get:
5(5x-7) = 7(2x+6)
simplify to get:
25x - 35 = 14x + 42
subtract 14x from both sides of this equation and add 35 to both sides of this equation to get:
11x = 77
divide both sides of this equation by 11 to get:
x = 7
substitute for x in either original equation to get:
y = 4
your solution is that x = 7 and y = 4.
you confirm by substituting for x and y in each original expression of the rectangle to get:
AB = 5x = 5*7 = 35
BC = 5y = 5*4 = 20
CD = 7y + 7 = 7*4 + 7 = 28 + 7 = 35
AD = 2x + 6 = 2*7 + 6 = 14 + 6 = 20
we know that AB is supposed to be equal to CD and BC is supposed to be equal to AD.
we get:
35 = 35 for AB equal to CD and we get:
20 = 20 for BC equal to AD.
everything checks out so the values of x and y are good.

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