Question

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 5 inches, and the length of the base is 2 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

Answer 1

Each congruent right triangle has legs 5 (altitude) and 1 (half the base), so each equal side = sqrt(5^2 + 1^2) = sqrt(26) ≈ 5.0990.
Perimeter = 2·sqrt(26) + 2 ≈ 2·5.0990 + 2 = 12.198 ≈ 12.2 inches.