Question

1. casey finds the unknown length of a rectangle. explain his strategy.

the area is 200 sq cm.

1. a rectangular garden has an area of 360 square meters. the width is 9 meters. what is the length of the garden?
2. rectangle a has a length of 8 centimeters and a width of 3 centimeters.

rectangle b is 5 times as long and 2 times as wide as rectangle a.
a. what is the length and width of rectangle b?
b. what is the area of rectangle b?

Explanation:

8. Explanation of Casey's strategy

Casey uses the formula for the area of a rectangle \(A = l\times w\) (where \(A\) is area, \(l\) is length, and \(w\) is width). He substitutes the known values (width \(w = 5\) cm and area \(A=200\) \(cm^{2}\)) into the formula \(r\times5 = 200\) (letting \(r\) be the unknown length). Then, he solves for \(r\) by dividing both sides of the equation by \(5\) (\(r=\frac{200}{5}=40\)).

Step1: Use the area formula

The formula for the area of a rectangle is \(A=l\times w\). We know \(A = 360\) \(m^{2}\) and \(w = 9\) m.

Step2: Solve for length \(l\)

We can rewrite the formula as \(l=\frac{A}{w}\). Substitute \(A = 360\) and \(w = 9\) into the formula: \(l=\frac{360}{9}\).

Step3: Calculate the value

\(\frac{360}{9}=40\)

Step1: Find the length of rectangle B

Given that rectangle B is \(5\) times as long as rectangle A. If the length of rectangle A is \(l_{A}=8\) cm, then the length of rectangle B, \(l_{B}=5\times l_{A}\). Substitute \(l_{A} = 8\) into the formula: \(l_{B}=5\times8 = 40\) cm.

Step2: Find the width of rectangle B

Given that rectangle B is \(2\) times as wide as rectangle A. If the width of rectangle A is \(w_{A}=3\) cm, then the width of rectangle B, \(w_{B}=2\times w_{A}\). Substitute \(w_{A}=3\) into the formula: \(w_{B}=2\times3=6\) cm.

Answer:

Casey uses the area formula \(A = l\times w\), substitutes known values, and solves the resulting equation for the unknown length.

9. Length of the rectangular garden