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
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.
