Geometry Question

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 26 inches, and the length of the base is 9 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

Answer 1

Half of the base = 9/2 = 4.5

Side = hypotenuse of half of the original triangle

= √(26*26 + 4.5*4.5)

2 * side + base ≈ 61.8 inches, rounded to the nearest tenth of an inch.

Answer 2

Use the altitude and the (1/2) base to find the side using the Law of Pythagoras.

Then the perimeter will be twice the side plus the base.