The triangle below is equilateral. Find the length of side x in simplist radical form with a rational denominator.
1 answer:
The most appropriate choice for equilateral triangle will be given by
Value of x =
What is equilateral triangle?
A closed two dimensional figure with three sides and three angles is called triangle.
Based on sides of triangle, triangle can be classified as equilateral, isosceles and scalene
The triangle whose all sides and all angles are equal is called equilateral triangle. All the angles of equilateral triangle are 60°
Here,
Since the triangle is equilateral, angle of triangle is 60°
sin 60° =
=
To learn more about equilateral triangle, refer to the link:
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Part A:
The first step of completing the square is writing the expression
as 
which expands to 
.
We have the first two terms exactly the same with the function we start with:
and 
but we need to add/subtract from the last term, 49, to obtain 41.
So the second step is to subtract -8 from the expression
The function in completing the square form is
Part B:
The vertex is obtained by equating the expression in the bracket from part A to zero
It means the curve has a turning point at x = -7
This vertex is a minimum since the function will make a U-shape.
A quadratic function
can either make U-shape or ∩-shape depends on the value of the constant 
that goes with . When is (+), the curve is U-shape. When (-), the curve is ∩-shape
Part C:
The symmetry line of the curve will pass through the vertex, hence the symmetry line is
This function is shown in the diagram below
The first step of completing the square is writing the expression
We have the first two terms exactly the same with the function we start with:
So the second step is to subtract -8 from the expression
The function in completing the square form is
Part B:
The vertex is obtained by equating the expression in the bracket from part A to zero
It means the curve has a turning point at x = -7
This vertex is a minimum since the function will make a U-shape.
A quadratic function
Part C:
The symmetry line of the curve will pass through the vertex, hence the symmetry line is
This function is shown in the diagram below