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miss Akunina [59]
3 years ago
8

The altitude of an equilateral triangle is 4.5 in. Find it's sides.

Mathematics
2 answers:
Mrrafil [7]3 years ago
4 0

Answer:

The length of each side is 3√3 in  or 5.20 in to the nearest hundredth.-

Step-by-step explanation:

The altitude splits up the triangle into two 30-60-90 triangles.

The ratio of the sides of these triangles is 2:1:√3.

The ratio of the altitude to the hypotenuse ( which is the side of the equilateral triangle ) = √3 : 2 so we have the equation:

2  / √3 = h / 4.5  where h is the required side.

h = 2*4.5 / √3

= 9 /√3

= 3 √3

= 5.196 in.

never [62]3 years ago
3 0

Answer:

Step-by-step explanation:

Let the length of each side be x. We can divide the triangle into two to get two right angled triangles which side will be x (hypotenuse), 4.5 (height), x/2 for base.

Using Pythagoras's theorem

x² = 4.5² + (x/2)²

x² = 81/4 + x²/4

x² - x²/4 = 81/4

3/4x² = 81/4

x² = 27

x = √27 = 3√3 in

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