A rectangle has area and length. Find the width. Area=27t^2-18t , Length= 9t.

Question:

A rectangle has area and length. Find the width. {eq}Area=27t^2-18t , Length= 9t. {/eq}

Area of a Rectangle

A rectangle is a quadrilateral that is also equiangular defined by its length and width. The area of a rectangle is the product of the length and the width.

Answer and Explanation:

The area of the rectangle, {eq}A_{\square} {/eq}, is given by the expression {eq}27t^{2}- 18t {/eq}. The length is {eq}9t {/eq}.

The equation for the area of a rectangle, {eq}A_{\square} {/eq} is:

{eq}A_{\square} = l \times w {/eq}

From here the width, {eq}w {/eq}, can be determined by dividing both sides by the length:

{eq}\displaystyle \frac{A_{\square}}{l} = w \ or \ w = \frac{A_{\square}}{l} {/eq}

Using the given expressions above:

{eq}\displaystyle w = \frac{27t^{2}- 18t}{9t} {/eq}

Factoring the numerator:

{eq}\displaystyle w = \frac{(9t)(3t-2)}{9t} {/eq}

This leaves:

{eq}w = 3t -2 {/eq}

Thus, the rectangle with an area of {eq}27t^{2}- 18t {/eq} and a length of {eq}9t {/eq} has a width of {eq}3t -2 {/eq}.


Learn more about this topic:

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Measuring the Area of a Rectangle: Formula & Examples

from Geometry: High School

Chapter 8 / Lesson 7
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