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 5 inches, and the length of the base is 2 inches. find the triangle’s perimeter. round to the nearest tenth of an inch.

Explanation:

Step1: Find half - base length

Since the altitude cuts the base into two equal segments and the base length is 2 inches, the half - base length $b=\frac{2}{2}=1$ inch.

Step2: Use Pythagorean theorem to find side length

In one of the right - triangles formed by the altitude, let the side length of the isosceles triangle be $s$. By the Pythagorean theorem $s=\sqrt{5^{2}+1^{2}}=\sqrt{25 + 1}=\sqrt{26}\approx5.1$ inches.

Step3: Calculate the perimeter

The perimeter $P$ of an isosceles triangle with two equal sides of length $s$ and base of length $B$ is $P = 2s + B$. Substituting $s\approx5.1$ inches and $B = 2$ inches, we get $P=2\times5.1+2=10.2 + 2=12.2$ inches.

Answer:

$12.2$ inches