Question 850975
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 + 7 = 3x + 2}}} Plug in AB = 2x + 7 and CD = 3x + 2


now we solve for x


{{{2x+7=3x+2}}} Start with the given equation.



{{{2x=3x+2-7}}} 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=(-5)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{x}}}.



{{{x=5}}} Reduce.


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


{{{BC = 3x + 4}}}



{{{BC = 3(5) + 4}}} Plug in {{{x = 5}}} we found above



{{{BC = 15 + 4}}}



{{{BC = 19}}}



Since {{{DA = BC}}}, we know that {{{DA = 19}}} also.


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Summary:


<font size=4 color="red">x = 5</font>


<font size=4 color="red">DA = 19</font>