Final answer:
The perimeter of the composite shape made of an equilateral triangle and a half circle with side lengths of 25 is found by adding the perimeters of both shapes. The correct perimeter is 75 + 12.5π using an approximation for π of 3.14. Therefore, the answer is option 1) 75 + 12.5π.
Step-by-step explanation:
The student's question involves calculating the perimeter of a shape that consists of an equilateral triangle attached to a half circle, with both shapes having specific known dimensions. In mathematics, we can find the perimeter of such a composite figure by adding the perimeters of the individual shapes that make it up. Since the triangle is equilateral, all three sides are equal, with each being 25 units long. The perimeter of the triangle is therefore 3 times 25, which totals 75 units.
For the half circle, we need to use the formula for a circle's circumference, which is 2πr, where π is approximately 3.14 and r is the radius. However, since we're dealing with a half circle, we'll use half of that formula. The triangle's side length is equal to the diameter of the half circle (25 units), which means the radius of the circle is half of that, or 12.5 units. The perimeter of the half circle is hence 12.5π. Adding the two perimeters together gives us the total perimeter of the composite shape: 75 + 12.5π which, using the given approximation for π (3.14), we can see matches option 1) 75 + 12.5π.