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 21 inches, and the length of the base is 18 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

Answer 1

Since the altitude cuts the base into two equal segments, each segment will have a length of 9 inches.

Now, using the Pythagorean Theorem in one of the congruent triangles, we can find the length of each leg:
a^2 + b^2 = c^2
9^2 + x^2 = 21^2
81 + x^2 = 441
x^2 = 360
x = √360
x ≈ 18.97

This means that each leg of the triangle is approximately 18.97 inches long.

Now we can find the perimeter of the triangle:
Perimeter = 18 + 18.97 + 18.97
Perimeter = 54.94 inches

Therefore, the perimeter of the isosceles triangle is approximately 54.9 inches.