Final answer:
To find the perimeter of the isosceles triangle, you can use the Pythagorean theorem to find the length of the congruent sides and then calculate the perimeter using the given base length. The perimeter of the triangle is approximately 60.3 inches.
Step-by-step explanation:
To find the perimeter of the isosceles triangle, we need to find the lengths of the congruent sides. Since the altitude cuts the base into two equal segments, each segment is 11/2 = 5.5 inches long. Using the Pythagorean theorem, we can find the length of the congruent sides as follows:
Let x be the length of each congruent side. Then, using the Pythagorean theorem, we have:
x^2 = 24^2 + 5.5^2
x^2 = 576 + 30.25
x^2 = 606.25
x = sqrt(606.25) = 24.63 inches
Since the triangle has two congruent sides, the perimeter of the triangle is given by:
Perimeter = 2x + 11
Perimeter = 2(24.63) + 11
Perimeter = 49.26 + 11
Perimeter = 60.26 inches (rounded to the nearest tenth of an inch).