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 15 inches, and the length of the base is 11 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 11 inches, the half - base length $b=\frac{11}{2}=5.5$ inches.

Step2: Use Pythagorean theorem to find the length of the equal sides

Let the length of each of the equal sides of the isosceles triangle be $s$. By the Pythagorean theorem $s=\sqrt{15^{2}+5.5^{2}}=\sqrt{225 + 30.25}=\sqrt{255.25}\approx15.98$ 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 $s\approx15.98$ inches and $B = 11$ inches, we get $P=2\times15.98+11=31.96 + 11=42.96\approx43.0$ inches.

Answer:

43.0 inches