Identify the perimeter and area of an equilateral triangle with height 12√2cm. give your answer in simplest radical form.

(D) P=24√6,  A=96√3

Step-by-step explanation:

Consider ΔABC where D is the midpoint of BC. Since ABC is an equilateral triangle, then segment AD is a perpendicular bisector with length of 12√2.   This creates ΔADC which is a 30°-60°-90° triangle.

Now you can use the rules for this special triangle to find the length of the hypotenuse.

30° ⇄ side length "a"        base - DC on ΔADC

60° ⇄ side length "a√3"   height - AD on ΔADC

90° ⇄ side length "2a"      hypotenuse - AC on ΔADC

Step 1: solve for "a"

Step 2: solve for "2a"

Step 3: find the perimeter

The side length is equivalent for all 3 sides so

P = 3(AC)

Step 4: find the area