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 11 inches, and the length of the base is 6 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

Answer 1

To find the perimeter of the isosceles triangle, we need to find the lengths of the two congruent triangles.

Since the altitude cuts the base into two equal segments, each segment will be 3 inches. Let's call the length of each congruent triangle's hypotenuse x.

Using the Pythagorean theorem on one of the congruent triangles, we have:
(3)^2 + (x)^2 = (11)^2
9 + x^2 = 121
x^2 = 112
x = √112
x ≈ 10.6 inches

Therefore, the perimeter of the triangle is:
perimeter = 2(10.6) + 6
perimeter ≈ 27.2 inches

So, the perimeter of the isosceles triangle is approximately 27.2 inches.