Math Problem Statement

My rectangular soccer field site has a length equal to one and a half times its width. Find its area in terms of its length x.

Solution

Let the width of the rectangular soccer field be denoted by ww, and the length by xx. According to the problem, the length is one and a half times the width:

x=32wx = \frac{3}{2} w

To express the width in terms of the length xx, solve for ww:

w=23xw = \frac{2}{3} x

The area AA of the rectangular soccer field is given by the product of the length and width:

A=x×wA = x \times w

Substituting w=23xw = \frac{2}{3} x into the equation for area:

A=x×23x=23x2A = x \times \frac{2}{3} x = \frac{2}{3} x^2

Thus, the area of the soccer field in terms of its length xx is:

A=23x2A = \frac{2}{3} x^2

Would you like more details or have any questions about this? Here are some related questions for further exploration:

  1. What is the width of the field if the length is 90 meters?
  2. How would the area formula change if the length were twice the width?
  3. What is the perimeter of the field in terms of xx?
  4. If the area is 5400 square meters, what is the length of the field?
  5. How would the area change if the length were increased by 20%?

Tip: When working with ratios, always solve for one variable in terms of the other to make calculations easier.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Algebra
Ratios

Formulas

Area of a rectangle: A = length × width
Relationship between length and width: x = 1.5w

Theorems

-

Suitable Grade Level

Grades 6-8