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 25 inches, and the length of the base is 20 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 first need to find the length of the two congruent sides.

Let x be the length of each congruent side.

Since the altitude cuts the base into two equal segments, each segment has a length of 10 inches.

We can now use the Pythagorean theorem to find the length of the congruent sides:

x^2 + 10^2 = 25^2
x^2 + 100 = 625
x^2 = 525
x = √525
x ≈ 22.9 inches

Now that we have found the length of the congruent sides, we can find the perimeter of the triangle:

Perimeter = 20 + 22.9 + 22.9
Perimeter ≈ 65.8 inches

Therefore, the perimeter of the isosceles triangle is approximately 65.8 inches.