Final answer:
To find out the size that Matt must use for the platform, we convert the scale measurements to actual dimensions. The platform's length needs to be 12 feet and the width needs to be 8 feet, based on the given scale of 2.5 inches to 2 feet.
Step-by-step explanation:
In order to solve the problem Matt faces with his scale drawing for the platform, we need to convert the measurements given in inches on the drawing to the actual size in feet. Based on the scale of 2.5 inches representing 2 feet, we can set up a proportion to find the required length in feet for the platform. The scale is given as 2.5 inches : 2 feet. Therefore, to find out the length and width in feet, we divide the measured length and width in inches by 2.5 and then multiply by 2.
For the length which is 15 inches on the scale drawing:
Length in feet = (15 inches / 2.5 inches) * 2 feet = 6 * 2 feet = 12 feet
For the width which is 10 inches on the scale drawing:
Width in feet = (10 inches / 2.5 inches) * 2 feet = 4 * 2 feet = 8 feet
The actual dimensions Matt must use for the platform are 12 feet in length and 8 feet in width.
To review similar problems, you would follow the same method of setting up a proportion using the scale factor, ensuring consistent units, and then solving for the measurement needed.
For example, if Haley's school building is 30 feet high and her scale model used a scale of 1 inch = 6 feet, then converting the height for the scale model would involve dividing the actual height by the scale factor:
Height in the scale model = 30 feet / 6 feet/inch = 5 inches