Question

Find the perimeter of an equilateral triangle that has an altitude of 21 in. Round your answer to the nearest whole number.

Answer 1

Answer:

Perimeter = 73 inches

Step-by-step explanation:

The attitude of an equilateral triangle divide the base in half which is the side of the triangle.  so c = x the hypotenuse, the base = 1/2x , attitude = 21

Using a² + b² = c²   let a = 21  c = x and b = 1/2x  

21² + (1/2x)² = x²

441 +1/4x² = x²

1764 +  x² = 4x²     Multiply all terms by 4

1764 = 4x²- x²

1764 = 3x²

588 = x²

$\sqrt{588} = x$              This is the length of a side

Now Perimeter = 3s

                            $3(\sqrt{588} )$

            Perimeter = 72.7461

             Perimeter = 73 inches