Respuesta :
Answer:
[tex]\text{The width of rectangle}=9x\text{ meters}[/tex]
Step-by-step explanation:
We have been given that the rectangle has an area of [tex]18x^3[/tex] square meters and a length of [tex]2x^{2}[/tex]. We are asked to find the width of rectangle.
Since we know that area of a rectangle is width times length of the rectangle, so we can find width of our given rectangle by dividing given area by length of rectangle.
[tex]\text{Area of rectangle}=\text{Width of rectangle *Length of the rectangle}[/tex]
[tex]\frac{\text{Area of rectangle}}{\text{Length of rectangle}}=\frac{\text{Width of rectangle *Length of the rectangle}}{\text{Legth of rectangle}}[/tex]
[tex]\text{The width of rectangle}=\frac{\text{Area of rectangle}}{\text{Length of rectangle}}[/tex]
Upon substituting our given values in above formula we will get,
[tex]\text{The width of rectangle}=\frac{18x^3\text{ meter}^2}{2x^2\text{ meters}}[/tex]
[tex]\text{The width of rectangle}=\frac{9x^3\text{ meters}}{x^2}[/tex]
Using exponent rule for quotient [tex]\frac{a^m}{a^n}=a^{m-n}[/tex] we will get,
[tex]\text{The width of rectangle}=9x^{3-2}\text{ meters}[/tex]
[tex]\text{The width of rectangle}=9x^{1}\text{ meters}=9x\text{ meters}[/tex]
Therefore, width of our given rectangle will be 9x meters.
