Question

Need Help
In isosceles ΔABC, AC = BC, AB = 6 in,
CD ⊥ AB, and CD = 3 in. Find the perimeter of the isosceles triangle.

Answer 1

2x+6=y
triangle ADC=x+3+3=y
triangle CBD=x+3+3=y
this is not possible until u give perimeter 

Answer 2

Answer:

$2\sqrt{18}+6 \ in$

Step-by-step explanation:

As ABC is an isosceles triangle, the segment CD cuts to AB in two equal parts. Then, AD=DB=3 in. Now, using Pitagoras Theorem we have that:

$CD^2+DB^2 = BC^2$

$3^2+3^2 = BC^2$

$BC = \sqrt{3^2+3^2}$

$BC = \sqrt{9+9}$

$BC = \sqrt{9+9}$

$BC = \sqrt{18}=AC$.

Now, the perimeter is the sum of the three sides of the triangle, then

$perimeter = AC+BC+AB = \sqrt{18}+\sqrt{18}+6 = 2\sqrt{18}+6 \ in$.