The altitude of an equilateral triangle is the square root of 6 units. What is the area of the triangle, in square units? Express your answer in simplest radical form.
+9466 Let x be the side length of the triangle. Here's a quick drawing:
From the Pythagorean theorem...
(x/2)2 + (√6)2 = x2
x2/4 + 6 = x2 Multiply through by 4 .
x2 + 24 = 4x2 Subtract x2 from both sides.
24 = 3x2 Divide both sides by 3 then take the positive square root of both sides.
x = √8
And...
area of triangle, in square units = (1/2)(x)(√6) = (1/2)(√8)(√6) = (1/2)(4√3) = 2√3
+9466 Let x be the side length of the triangle. Here's a quick drawing:
From the Pythagorean theorem...
(x/2)2 + (√6)2 = x2
x2/4 + 6 = x2 Multiply through by 4 .
x2 + 24 = 4x2 Subtract x2 from both sides.
24 = 3x2 Divide both sides by 3 then take the positive square root of both sides.
x = √8
And...
area of triangle, in square units = (1/2)(x)(√6) = (1/2)(√8)(√6) = (1/2)(4√3) = 2√3
