SOLUTION: We're suppose to use the properties of rectangles to solve Rectangle ABCD, but the book doesn't provide any clue on how to solve the problem. Given: AB = 2x + 7, BC = 3x + 4,

Algebra ->  Parallelograms -> SOLUTION: We're suppose to use the properties of rectangles to solve Rectangle ABCD, but the book doesn't provide any clue on how to solve the problem. Given: AB = 2x + 7, BC = 3x + 4,       Log On


   

Question 850975: We're suppose to use the properties of rectangles to solve Rectangle ABCD, but the book doesn't provide any clue on how to solve the problem.

Given: AB = 2x + 7, BC = 3x + 4, and CD = 3x + 2
Find: x and DA
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In every rectangle, the opposite sides are congruent (ie of the same length).

AB and CD are opposite sides. So AB = CD


AB+=+CD

2x+%2B+7+=+3x+%2B+2 Plug in AB = 2x + 7 and CD = 3x + 2

now we solve for x

2x%2B7=3x%2B2 Start with the given equation.


2x=3x%2B2-7 Subtract 7 from both sides.


2x-3x=2-7 Subtract 3x from both sides.


-x=2-7 Combine like terms on the left side.


-x=-5 Combine like terms on the right side.


x=%28-5%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=5 Reduce.

-------------------------------------------------------

Now AD or DA is opposite side BC. So the two sides are congruent. That means we need to find BC first

BC+=+3x+%2B+4


BC+=+3%285%29+%2B+4 Plug in x+=+5 we found above


BC+=+15+%2B+4


BC+=+19


Since DA+=+BC, we know that DA+=+19 also.

================================================================================================

Summary:

x = 5

DA = 19