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The area of a rectangle is represented by 36 x^{6} y^{4}. One side is represented by 6 x^{3} y^{2}. What is the length of the other side? What does this indicate about the type of rectangle represented?

The Area Of A Rectangle Is Represented By 36 X6 Y4 One Side Is Represented By 6 X3 Y2 What Is The Length Of The Other Side What Does This Indicate About The Typ class=

Answer :

Answer:

• 6x³y²

,

• Square

Explanation:

Area of a rectangle = Length x Width

If the area and one side of the rectangle is given:

[tex]\begin{gathered} \text{Area}=36x^6y^4 \\ \text{Length}=6x^3y^2 \end{gathered}[/tex]

We then have that:

[tex]36x^6y^4=6x^3y^2\times Width[/tex]

We solve the above for the length of the other side.

[tex]\begin{gathered} \text{Width}=\frac{36x^6y^4}{6x^3y^2} \\ =6x^3y^2 \end{gathered}[/tex]

We notice that the length of both sides is the same. Therefore, the type of rectangle represented is actually a square.

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