Question

sides of equilateral triangle abc touches the parabola y square equal to 4 x 10 point abc lie on

Answer 1

Answer:

A(0, 0), B(12, 6.928) and C(12, -6.928)

Step-by-step explanation:

In the picture we can se the graph of the functions

x = 12 and $y^{2}$ = 4$x$

As we can see they intersect in (12, 6.928) and (12, -6.928).

Lets consider the equilateral triangle has vertices in A(0, 0), B(12, 6.928) and C(12, -6.928). So, we just need to verify that all sides have the same measurement.

Then BC = 6.928 - (-6.928) = 13.856 units

Since the triangle is equilateral, we know that AB = AC.

By Pythagoras theorem, we have:

$AB^{2}$ = $12^{2} + 6.325^{2}$ = 191.997184

AB = $\sqrt{191.997184}$ = 13.856 units

Hence, we conclude that AB = AC = 13.856 and BC = 13.856.

Then the triangle is equilateral.

A(0, 0), B(12, 6.928) and C(12, -6.928)