Question

10. The triangle below is equilateral. Find the length of

side in simplest radical form with a rational
denominator.

Answer 1

x=
`5√(3)`

Explanation:

Given:

What is equilateral? Equilateral means that all sides are equal and all angles are congruent. This means that if one side is 10, then the other 2 sides are also 10.

Step 1:

Let's label the triangle. We'll call it triangle ABC, A being the top left point, B being the bottom point, and C being the top right. Let's also label the intersection between the two lines in the top middle as D.

Step 2:

We know AB=10, So therefore --> BC=10 --> AC=10

Step 3:

AC=10 --> AD=5, DC=5

Step 4:

Use Pythag. Pythag states: a^2+b^2=c^2

a=5, c=10, b=???

5^2+b^2=10^2

Step 5:
Use algebra. 25+b^2=100

b^2=75

`√(75)\\√(5*5*3)\\ 5√(3)`

Answer 2

5✓3

Explanation:

all sides are 10 units

we know that each interior angle is 60 and the perpendicular height is shown there.

the height line is 90 degrees and the interior is 60 so the other angle is 30 degrees.

each of them is a right triangle so we can use the angles to find the length.

we know that the opposite of 60 degrees is the half of the hypotenuse times sqr root 3

hypotenuse= 10

x= 5✓3