CalculatorUser

oh ok it makes sense to me now I didn't know how the point could be place sqrt(7) from the bottom side, it confused me.

woahhh waiting for moderation is annoying

Notice there are a lot of 90 degree triangles within the diagram,

I think you might have to create a system of equations that can solve for EC using pythagoream theorem knowing the length of DB and DC

Since triangle DBC is a 45 - 45 - 90 triangle.

Can you solve for the length sof BD and DC?

Call the center point X.

Quadrilateral AEXD has a total angle sum of 360 degrees.

Since XEA and XDA is 90 degrees, and angle A is 60 degrees.

This means that angle EXD is 90 + 90 + 60 + x = 360

240 + x = 360

x = 120

So angle EXD is 120 degrees.

Based on supplements, EXB is 60 degrees.

Triangles EXB and DXC are 30 60 90 triangles.

Can you find angles XBC and XCB?

Hint: you might need two variables and make a system of equations

Does this make sense I tried solving it but couldn't (I was confused how x can be root 7 distance away from BC)

Im confused which side is 7 and which side is 8.

Can we assume that the left and right is 7 and the top and bottom is 8?

fudge I accidently reloaded my page 2 times already, meaning that I had to re do my explanation two times.

calculate KBE

Base:

20/4 = 5

Height:

20

5 * 20 = 100 / 2 = 50

base of grey triangle is half of KBE, because BC is divided into 4 congruent parts, while LM, equal to BC, is divided into 8 parts.

So calculate grey triangle:

Base:

5/2 = 2.5

Height:

20 / 2 = 10

10 * 2.5 = 25/2 = 12.5

Count number of grey triangles. 8 triangles

So 12.5 * 8 = 100

It intersects one time if they have ONE solution.

We substitute Y.

\(x^2+a=ax\)

Then we set it equal 0 so it matches the standard quadratic form.

\(x^2-ax+a=0\)

In order to find when it has ONE solution, the discriminant of the equation ABOVE has to be equal to 0.

The discriminant is:

\(b^2-4ac\)

We plug in values.

\((-a)^2-4(a)=0\)

We have:

\(a^2-4a=0\)

We factor:

\(a(a-4)=0\)

a = 0 or a = 4

So the sum of the values is 0 + 4 = \(\boxed{4}\)

Can you post the image please, its always blocked on my computer.