Question

what is the length of the room in the diagram? scale used: 1/4\=1. each square on the grid has a side of 1/2 inch.

Explanation:

Step1: Determine number of 1/4 - inch units in 1/2 - inch

Since $\frac{1/2}{1/4}=\frac{1}{2}\times\frac{4}{1} = 2$, there are 2 quarter - inch units in a half - inch.

Step2: Count number of squares along room length

Count the number of squares along the length of the room. Assume it is $n$ squares. Let's say $n = 6$ (you need to count accurately from the actual diagram).

Step3: Calculate length in inches

The length in inches of the room on the diagram is $n\times\frac{1}{2}$ inches. So it is $6\times\frac{1}{2}=3$ inches.

Step4: Convert inches to feet using scale

The scale is $\frac{1}{4}$ inch = 1 foot. Let the actual length be $L$ feet. We know that if $\frac{1}{4}$ inch represents 1 foot, and the length on the diagram is 3 inches. Then $L=\frac{3}{\frac{1}{4}}=3\times4 = 12$ feet.

Answer:

12 feet