Answer:
<h3>a)a+c=150,10.25a+7.75c=1470</h3>
Step-by-step explanation:
<h3>to understand this</h3><h3>you need to know about:</h3>
- system of linear equation
<h3>let's solve:</h3>
according to the first condition
according to the second condition
bearing in mind that a solution to a system of equations is where their graph intersect or meets, Check the picture below.
We know that
[area of a regular hexagon]=6*[area of one <span>equilateral triangle]
</span>210.44=6*[area of one equilateral triangle]
[area of one equilateral triangle]=210.44/6-----> 35.07 cm²
[area of one equilateral triangle]=b*h/2
h=7.794 cm
b=2*area/h------> b=2*35.07/7.794------>b= 9 cm
the length side of a regular hexagon is 9 cm
<span>applying the Pythagorean theorem
</span>r²=h²+(b/2)²------>r²=7.794²+(4.5)²------> r²=81--------> r=9 cm
<span>this last step was not necessary because the radius is equal to the hexagon side------> (remember the equilateral triangles)
</span>
the answer is
the radius is 9 cm