The area of a rectangle is 30 m^2. If the length is the square root of 75, what is the width?

Question:

The area of a rectangle is 30 m{eq}^{2} {/eq}.

If the length is the square root of 75, what is the width?

The Area of a Rectangle:

  • A rectangle is a plane figure that has two pairs of opposite and parallel sides. The opposite sides of a rectangle are congruent.
  • The area of a rectangle is the amount of space covered by the figure. It is given by {eq}A = l\times w {/eq}, where {eq}l {/eq} is the length and {eq}w {/eq} is the width.

Answer and Explanation:


The area of a rectangle is given by:

  • {eq}A = l\times w {/eq}

where {eq}l {/eq} is the length and {eq}w {/eq} is the width of the rectangle.

If the area of a rectangle is {eq}A = 30\; \rm m^2 {/eq} and the length is {eq}l = \sqrt{75} {/eq}, then:

  • {eq}30 = \sqrt{75}w {/eq}

Solving for {eq}w {/eq}, we get:

  • {eq}w = \dfrac{30}{\sqrt{75}}\; \rm m {/eq}
  • {eq}w = \dfrac{30}{5\sqrt{3}}\; \rm m {/eq}
  • {eq}\boxed{\color{blue}{w = \dfrac{6}{\sqrt{3}}\; \rm m}} {/eq}
  • {eq}\boxed{\color{blue}{w \approx 3.641\; \rm m}} {/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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