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 18 inches, and the length of the base is 15 inches. find the triangles perimeter. round to the nearest tenth of an inch. answer attempt 1 out of 2 in. submit answer show examples

Explanation:

Step1: Find the length of the equal - sides of the isosceles triangle

Since the altitude of an isosceles triangle bisects the base. Let the base \(b = 15\) inches, so each half of the base \(x=\frac{15}{2}=7.5\) inches. The altitude \(h = 18\) inches.
Using the Pythagorean theorem \(a=\sqrt{x^{2}+h^{2}}\), where \(a\) is the length of the equal - sides of the isosceles triangle.
Substitute \(x = 7.5\) and \(h=18\) into the formula:
\(a=\sqrt{7.5^{2}+18^{2}}=\sqrt{56.25 + 324}=\sqrt{380.25}=19.5\) inches.

Step2: Calculate the perimeter of the triangle

The perimeter \(P\) of a triangle with sides \(a,a,b\) (for an isosceles triangle) is \(P=2a + b\).
Substitute \(a = 19.5\) and \(b = 15\) into the formula:
\(P=2\times19.5+15=39 + 15=54.0\) inches.

Answer:

\(54.0\)