Final answer:
The dimensions of the rectangle on a scale drawing, given an actual size of 50 feet by 30 feet and a scale of 1/2 inch equals 5 feet, would be 5 inches in length and 3 inches in width when using proportions to determine the scaled measurements.
Step-by-step explanation:
The question asks to calculate the dimensions of a rectangle given the scale and the actual dimensions. To determine the length and width of the rectangle on a scale drawing where the unit scale is 1/2 inch equals 5 feet, we use proportions based on the actual dimensions of Rano's backyard, which are 50 feet by 30 feet.
For the length: Actual length is 50 feet. The scale is 1/2 inch to 5 feet, so we set up the proportion as follows:
Length = (1/2 inch) / 5 feet = 0.5 inches / 50 feet
After calculating this proportion, the length on the scale drawing will be 5 inches (since 50 feet is 10 times the scale factor of 5 feet).
Similarly, for the width: Actual width is 30 feet.
Width = (1/2 inch) / 5 feet = w / 30 feet
After solving this proportion, the width on the scale drawing will be 3 inches (since 30 feet is 6 times the scale factor of 5 feet).