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 18 inches. find the triangles perimeter. round to the nearest tenth of an inch.

Explanation:

Step1: Find the length of one of the equal sides

Since the base is \(18\) inches and the altitude cuts the base into two equal segments, each segment is \(\frac{18}{2}=9\) inches.
Let the length of one of the equal sides of the isosceles triangle be \(l\). Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 9\) (half - base), \(b=20\) (altitude), and \(c\) is the length of the equal side.
So, \(l=\sqrt{9^{2}+20^{2}}=\sqrt{81 + 400}=\sqrt{481}\approx21.9\)

Step2: Calculate the perimeter

The perimeter \(P\) of the isosceles triangle is \(P=2l+18\).
Substitute \(l\approx21.9\) into the formula: \(P = 2\times21.9+18=43.8+18=61.8\)

Answer:

\(61.8\)