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# Analytic Geometry

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The area of rectangle ABCD with vertices A(0, 0), B(0, 4), C(x, 4) and D(x, 0) is $$16$$ square units. If x > 0, what is the value of x?

Apr 13, 2022

#1
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From the information given above, we can say that the width of the rectangle is $$4$$

The area of a rectangle is $$length \cdot width$$

That is, $$4 \cdot length = 16$$

That gives us length = $$16/4 = 4$$

From that, we can tell that the value of $$x$$ must be $$4$$.

Apr 13, 2022
#2
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I'm pretty sure that 4 is the answer, but....hold up

Wouldn't that make it a square though??

Vinculum  Apr 13, 2022
#4
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But, a square is technically a rectangle... So your answer would still be right.

BuilderBoi  Apr 13, 2022
#3
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Yes i think so

Apr 13, 2022
#5
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Note that  a square is a special case of a  rectangle....but a rectangle isn't necessarily a square   Since AB  = 4 ....then  it must also be that BC = 4

So....the area  =  (AB) (BC) =  (4)(4)  =  16   Apr 13, 2022
#6
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Good Job vin

Apr 13, 2022