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

`2√(18)+6 \ in`

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 = √(3^2+3^2)`

`BC = √(9+9)`

`BC = √(9+9)`

`BC = √(18)=AC`.

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

`perimeter = AC+BC+AB = √(18)+√(18)+6 = 2√(18)+6 \ in`.