Question

1. a rectangular field has an area of 2100 square feet. the length of the field is 50 feet.

a. how wide is the field?
b. the field is divided into 3 rectangles, as shown. write and solve an equation for x.
c. determine the dimensions of each rectangle.

1. the class took a quiz. the average of 4 quizzes was 74. al scored a 92, bob scored a 45, and john scored a 76. what score did jill earn?
2. the sum of the measures of the interior angles of that triangle is 180°. write and solve an equation to find the value of the variable.

Explanation:

14.

a.

Step1: Recall the area formula for a rectangle

The area formula for a rectangle is \(A = l\times w\), where \(A\) is the area, \(l\) is the length, and \(w\) is the width. We know that \(A = 2100\) square feet and \(l=50\) feet.

Step2: Solve for the width \(w\)

Using the formula \(w=\frac{A}{l}\), substitute \(A = 2100\) and \(l = 50\). So \(w=\frac{2100}{50}=42\) feet.

Step1: Express the total width in terms of \(x\)

The total width of the field is \(x + 3x+2x\). From part (a), we know the total width is \(42\) feet. So the equation is \(x + 3x+2x=42\).

Step2: Combine like - terms and solve for \(x\)

Combine like - terms: \(6x = 42\). Then divide both sides by \(6\): \(x=\frac{42}{6}=7\).

Step1: Find the dimensions of each rectangle

For the first rectangle: length \(l = 50\) feet and width \(w=x\). Since \(x = 7\), the dimensions are \(50\times7\) feet.
For the second rectangle: length \(l = 50\) feet and width \(w = 3x\). Substitute \(x = 7\), then \(w=3\times7 = 21\) feet, and the dimensions are \(50\times21\) feet.
For the third rectangle: length \(l = 50\) feet and width \(w=2x\). Substitute \(x = 7\), then \(w=2\times7=14\) feet, and the dimensions are \(50\times14\) feet.

Answer:

The width of the field is \(42\) feet.

b.