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 21 inches, and the length of the base is 18 inches. find the triangle’s perimeter. round to the nearest tenth of an inch.

Explanation:

Step1: Find half - base length

The base is 18 inches, so half - base length $b=\frac{18}{2}=9$ inches.

Step2: Use Pythagorean theorem to find side length

Let the side length of the isosceles triangle be $s$. By the Pythagorean theorem $s=\sqrt{21^{2}+9^{2}}=\sqrt{441 + 81}=\sqrt{522}\approx22.85$ inches.

Step3: Calculate the perimeter

The perimeter $P$ of an isosceles triangle with two equal sides of length $s$ and base $B$ is $P = 2s + B$. Substituting $s\approx22.85$ inches and $B = 18$ inches, we get $P=2\times22.85+18=45.7+18 = 63.7$ inches.

Answer:

$63.7$ inches