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?

Explanation:

Step1: Find the scale factor

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

Step2: Find the actual dimensions of the office

The dimensions of the office in the scale - drawing are 2 cm by 4 cm.
The actual width: $2\times\frac{5}{2}=5$ feet.
The actual length: $4\times\frac{5}{2}=10$ feet.

Step3: Find the actual area of the office

The area formula is $A = lw$. Substitute $l = 10$ feet and $w = 5$ feet.
$A=10\times5 = 50$ square - feet.

Step4: Find the width of the couch on the scale - drawing

Let $x$ be the width of the couch on the scale - drawing.
We know that $\frac{x}{3}=\frac{6}{15}$. Cross - multiply: $15x=3\times6$.
$15x = 18$, then $x=\frac{18}{15}=1.2$ cm.

Answer:

1. The actual dimensions of the office are 5 feet by 10 feet.
2. The actual area of the office is 50 square feet.
3. The width of the couch on the scale - drawing is 1.2 cm.