Question

The altitude of an equilateral triangle is 12cm. How long is each side

Answer 1

The length of each side of the equilateral triangle is 12√3 cm.

Step-by-step explanation:

To find the length of each side of an equilateral triangle when the altitude is 12 cm, we can use the formula:

Side length = 2 * (altitude / √3)

Substituting the value given, we have:

Side length = 2 * (12 cm / √3)

Simplifying the expression, we get:

Side length = 12 cm * (√3 / √3)

Side length = 12 cm * (√3 / 1)

Side length = 12√3 cm

Therefore, each side of the equilateral triangle is 12√3 cm long.

Answer 2

Each side of the equilateral triangle is
`\( √(3) * \text{altitude} \)`, so each side is
`\( 12√(3) \)` cm.

Step-by-step explanation:

In an equilateral triangle, all sides are equal, and each angle measures 60 degrees. The altitude of the triangle bisects one of the angles, forming a right-angled triangle with half the equilateral side as the base, the altitude as one leg, and the side of the equilateral triangle as the hypotenuse.

Using the Pythagorean theorem, we find that the length of one side s is given by:

`\[ s = \sqrt{\text{altitude}^2 + \left((s)/(2)\right)^2} \]`

Substituting the given altitude value
`(\(12 \ \text{cm}\))`, we get:

`\[ s = \sqrt{12^2 + \left((s)/(2)\right)^2} \]`

Solving this equation yields
`\( s = 12√(3) \ \text{cm} \).`

Understanding the relationship between the altitude, sides, and angles of an equilateral triangle is fundamental in geometry, providing a basis for solving various geometric problems.