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 25 inches, and the length of the base is 20 inches. find the triangles 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 20 inches, the length of half - base $b=\frac{20}{2}=10$ inches.

Step2: Use Pythagorean theorem to find side length

Let the length of each of the equal sides of the isosceles triangle be $s$. According to the Pythagorean theorem $s=\sqrt{h^{2}+b^{2}}$, where $h = 25$ inches and $b = 10$ inches. So $s=\sqrt{25^{2}+10^{2}}=\sqrt{625 + 100}=\sqrt{725}=5\sqrt{29}\approx26.9$ inches.

Step3: Calculate the perimeter

The perimeter $P$ of an isosceles triangle is $P = 2s+20$. Substitute $s\approx26.9$ inches into the formula: $P=2\times26.9+20=53.8 + 20=73.8$ inches.

Answer:

73.8 inches