an altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent…

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.

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

Explanation:

Step1: Find half - base length

Since the altitude cuts the base into two equal segments and the base length is 15 inches, the length of each half - base is $\frac{15}{2}=7.5$ inches.

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 $l$. By the Pythagorean theorem $l=\sqrt{7.5^{2}+18^{2}}=\sqrt{56.25 + 324}=\sqrt{380.25}=19.5$ inches.

Step3: Calculate the perimeter

The perimeter $P$ of the isosceles triangle is $P = 2l+15$. Substitute $l = 19.5$ into the formula: $P=2\times19.5 + 15=39+15=54.0$ inches.

Answer:

54.0 inches