An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 36 inches, and the length of the base is 12 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.
First, we can determine the length of the legs of the isosceles triangle using the Pythagorean Theorem. Since the altitude divides the isosceles triangle into two congruent right triangles, the legs of each of these right triangles will be equal.
Let x be the length of each leg of the isosceles triangle. Using the Pythagorean Theorem, we have:
x^2 + 6^2 = 36^2
x^2 + 36 = 1296
x^2 = 1260
x = √1260
x ≈ 35.5 inches
Therefore, the perimeter of the isosceles triangle is:
Perimeter = 2x + 12
Perimeter = 2(35.5) + 12
Perimeter = 71 + 12
Perimeter = 83 inches
Therefore, the perimeter of the isosceles triangle is 83 inches.