An isosceles triangle

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 triangle's perimeter. Round to the nearest tenth of an inch.

Final Answer:

o =  54 in

Step-by-step explanation:

$$\begin{gathered} h=18\text{in} \\ a=15\text{in} \\ {b}^2=(a/2{)}^2+h^2 \\ b=\sqrt{(a/2{)}^2+h^2}=\sqrt{(15/2{)}^2+18^2}=\frac{39}{2}=19.5\text{in} \\ c=b=19.5=\frac{39}{2}=19.5\text{in} \\ o=a+b+c=15+19.5+19.5=54\text{in} \end{gathered}$$

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