Question

Brody measured a house and its lot and made a scale drawing. He used the scale 3 inches : 2 feet. If the actual length of the backyard is 48 feet, how long is the yard in the drawing?

Answer 1

To find the length of the backyard in the scale drawing, first find the scale factor from the given scale 3 inches : 2 feet. Then, convert the actual length of 48 feet to inches and multiply by the scale factor. The resulting length of the backyard in the drawing will be 24 inches.

Step-by-step explanation:

To calculate how long the backyard should be in the scale drawing that Brody is making, we use the scale 3 inches : 2 feet. This means that for every 3 inches on the drawing, the actual length is 2 feet. Since the actual length of Brody's backyard is 48 feet, we first need to figure out the scale factor and then use this to find the length on the drawing.

Step-by-Step Solution:

1. Write the scale as a ratio: 3 inches/2 feet.
2. Since 2 feet is equal to 24 inches (1 foot = 12 inches), rewrite the ratio with both measurements in the same units: 3 inches/24 inches.
3. Divide both numbers by 3 to find the scale factor: 1/8.
4. Now, calculate the length on the drawing by multiplying the actual length by the scale factor: 48 feet (actual length) × 1/8 (scale factor).
5. Convert the actual length into inches before multiplying: 48 feet x 12 inches/foot = 576 inches.
6. Finally, multiply 576 inches by the scale factor 1/8 to get the drawing length: 576 × 1/8 = 72 inches.
7. Convert the length on the drawing back to inches: 72 inches is equivalent to 72/3 = 24 inches, since 3 inches in the drawing represent 1 inch of actual length.

So, the length of the backyard in the drawing will be 24 inches.