Answer:
=6√3 the third option.
Step-by-step explanation:
We can use the Pythagoras theorem to find the value of y. We need two equations that include y.
a²+b²=c²
c=9+3=12
x²+y²=12²
x²=144 - y².........i (This is the first equation)
We can also express it in another way but let us find the perpendicular dropped to c.
perpendicular²= x²-3²=x²-9 according to the Pythagoras theorem.
y²=(x²-9)+9²
y²=x²+72
x²=y²-72....ii( this is the second equation
Let us equate the two.
y²-72=144-y²
2y²=144+72
2y²=216
y²=108
y=√108
In Surd form √108=√(36×3)=6√3
y=6√3
 
        
             
        
        
        
Answer:
The perimeter of the base of the birdhouse is 36 units
Step-by-step explanation:
<u><em>The complete question is</em></u>
Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the measure of the exterior angle and the length of a diagonal that passes through the center is 12. What is the perimeter of the base of the birdhouse?
step 1
Find the measure of the interior angle
Let
x ---> the measure of the interior angle
y ---> the measure of the exterior angle
Remember that
the sum of the interior and exterior angle in any polygon is equal to 180 degrees
so
 ----> equation A
 ----> equation A
we have that
the measure of the interior angle is twice the measure of the exterior angle
so
 ----> equation B
 ----> equation B
substitute equation B in equation A


so

That means-----> The figure is a regular hexagon
step 2
Remember that
The length of the diagonal that passes through the center of the hexagon is equal to two times the length of the regular hexagon 
Let
 b ----> the length side of the hexagon
so

The perimeter of the hexagon is given by the formula

substitute

 
 
        
             
        
        
        
It's 13000, just think about it....