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 13 inches, and the length of the base is 8 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

Answer 1

Let's call the length of each leg of the isosceles triangle "x". Since the altitude splits the triangle into two congruent right triangles, we know that the length of one leg of each right triangle is 4 (half of the base, which is 8). Using the Pythagorean theorem, we can solve for the length of the other leg:

x^2 = 13^2 + 4^2
x^2 = 185
x ≈ 13.6

Now we can find the perimeter of the whole triangle:

P = 2x + 8
P = 2(13.6) + 8
P ≈ 35.2

Rounding to the nearest tenth of an inch, the perimeter is 35.2 inches.