Question

1. here is the whole floor that zahras office is on. each room is a scaled copy of every other room. the scale for this blueprint is 6 centimeters to 15 feet. use any strategy to determine the actual area of the room with the question mark.

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: Determine the dimensions of the room on the blueprint

Let's assume we can find the length and width of the room with the question - mark on the blueprint. Suppose the length $l$ and width $w$ of the room on the blueprint are measured (not given in the problem description, but if we assume we have them). Let's say the length on the blueprint is $l_{b}$ and the width on the blueprint is $w_{b}$.

Step3: Calculate the actual length and width

The actual length $L = l_{b}\times\frac{5}{2}$ feet and the actual width $W = w_{b}\times\frac{5}{2}$ feet.

Step4: Calculate the actual area

The actual area $A = L\times W=(l_{b}\times\frac{5}{2})\times(w_{b}\times\frac{5}{2})=\frac{25}{4}l_{b}w_{b}$ square feet.

Since the dimensions of the room on the blueprint are not given, if we assume the length on the blueprint $l_{b}=x$ cm and width on the blueprint $w_{b}=y$ cm, the actual area $A=\frac{25}{4}xy$ square feet. For example, if $x = 6$ cm and $y = 4$ cm:

Step1: Find the scale factor

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

Step2: Calculate actual length and width

Actual length $L=6\times\frac{5}{2}=15$ feet, actual width $W = 4\times\frac{5}{2}=10$ feet.

Step3: Calculate actual area

$A = 15\times10=150$ square feet.

Answer:

The actual area of the room is $\frac{25}{4}l_{b}w_{b}$ square feet, where $l_{b}$ and $w_{b}$ are the length and width of the room on the blueprint in centimeters. If specific blueprint - dimensions are given (e.g., $l_{b}=6$ cm and $w_{b}=4$ cm), the actual area is 150 square feet.