Question

problems 1-4: here is part of a scale drawing of zahras office. the scale is 6 centimeters to 15 feet. 1. what are the dimensions of the actual office? 2. what is the actual area of her office? 3. zahra wants to put a couch in her office that is 3 feet wide. how wide would the couch be if it were drawn on the scale drawing? 4. fabianas office is near zahras office and measures 4 centimeters by 8 centimeters in the scale drawing. is fabianas office twice the area of zahras office? explain your thinking.

Explanation:

Step1: Find the scale factor

The scale is 6 cm to 15 feet, so the scale - factor for length is $\frac{15}{6}=\frac{5}{2}$ feet per centimeter.

Step2: Find the actual dimensions of Zahra's office

The scale - drawing dimensions of Zahra's office are 2 cm by 4 cm.
The actual length $l = 2\times\frac{5}{2}=5$ feet and the actual width $w = 4\times\frac{5}{2}=10$ feet.

Step3: Calculate the actual area of Zahra's office

The area formula is $A=l\times w$. So, $A = 5\times10 = 50$ square feet.

Step4: Find the scale - drawing width of the couch

Let $x$ be the width of the couch on the scale - drawing. We know that $\frac{15}{6}=\frac{3}{x}$. Cross - multiplying gives $15x=18$, so $x = 1.2$ cm.

Step5: Find the actual dimensions of Fabiana's office

The scale - drawing dimensions of Fabiana's office are 4 cm by 8 cm.
The actual length $L = 4\times\frac{5}{2}=10$ feet and the actual width $W = 8\times\frac{5}{2}=20$ feet.
The actual area of Fabiana's office $A_{F}=10\times20 = 200$ square feet.
Since the area of Zahra's office is 50 square feet, and $200\div50 = 4$, Fabiana's office is 4 times the area of Zahra's office, not 2 times.

Answer:

1. The actual dimensions of Zahra's office are 5 feet by 10 feet.
2. The actual area of Zahra's office is 50 square feet.
3. The width of the couch on the scale - drawing is 1.2 cm.
4. No, Fabiana's office is 4 times the area of Zahra's office. The actual area of Fabiana's office is 200 square feet and the actual area of Zahra's office is 50 square feet.