Answer:
We can start by finding the length of each side of the triangle in the scale drawing, and then use the scale ratio to convert those lengths to actual feet.
From the scale drawing, we see that the length of the base of the triangle is 5 inches, and the length of one of the legs (the one with the angle marked as "yº") is also 5 inches. The length of the other leg is not given, but we can use the fact that the angles in a triangle add up to 180º to find it. The angle opposite the base of the triangle is 90º (since it is a right triangle), and the angle marked as "yº" is also given. So the third angle must be:
180º - 90º - yº = 90º - yº
Now we can use the fact that the angles of a triangle add up to 180º to write an equation involving the third angle and the angle opposite the other leg:
90º - yº + angle opposite other leg = 180º
Solving for the angle opposite the other leg, we get:
angle opposite other leg = yº
So the triangle is an isosceles right triangle, with legs of length 5 inches.
To find the actual length of each leg, we use the scale ratio of 1 in.: 1/1/2 ft 6 in. This means that every 1 inch in the scale drawing represents 1.5 feet in actual size. Therefore, each leg of the triangle is:
5 inches x 1.5 feet/1 inch = 7.5 feet
The base of the triangle is still 5 inches long, so it remains 5 inches long in actual size (since we have only multiplied by a factor of 1.5 in the conversion).
Finally, we can find the perimeter of the actual triangle by adding up the lengths of all three sides:
Perimeter = 7.5 feet + 7.5 feet + 5 inches x 1.5 feet/1 inch = 22.5 feet + 6.25 feet = 28.75 feet
Therefore, the perimeter of the actual triangle used on the banner is 28.75 feet.