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 Attempt 2out of 2 square in

## Step 1<br />The problem involves an isosceles triangle, which is a triangle with two equal sides. The altitude drawn from the vertex of the isosceles triangle forms two right-angled triangles. The altitude cuts the base into two equal segments, each of length 9 inches (since the total length of the base is 18 inches).<br /><br />## Step 2<br />We can use the Pythagorean theorem to find the length of the equal sides of the isosceles triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as:<br />### \(a^2 + b^2 = c^2\)<br />where \(a\) and \(b\) are the lengths of the two legs of the right triangle, and \(c\) is the length of the hypotenuse.<br /><br />## Step 3<br />In this case, the length of the altitude (21 inches) is one of the legs of the right triangle, and half of the base (9 inches) is the other leg. We can substitute these values into the Pythagorean theorem to find the length of the equal sides of the isosceles triangle:<br />### \(a = \sqrt{c^2 - b^2} = \sqrt{21^2 - 9^2}\)<br /><br />## Step 4<br />Once we have the length of the equal sides, we can find the perimeter of the isosceles triangle by adding the lengths of all three sides. The perimeter \(P\) is given by:<br />### \(P = 2a + b\)