Answer:
The correct options are 1, 2 and 4.
Step-by-step explanation:
The given triangle is an equilateral triangle. All the sides of an equilateral triangle are same. All interior angles are equal with measure 60 degree.
The distance from the center of an equilateral triangle to the midpoint of a side is known as apothem. In the given figure letter a represents the apothem.
Point D is the midpoint of BC,
[tex]b=\frac{BC}{2}=\frac{8.7}{2}=4.35[/tex]
Use Pythagorean theorem in triangle COD. So, option 1 is correct.
[tex]OC^2=OD^2+DC^2[/tex]
[tex]5^2=a^2+(4.35)^2[/tex]
[tex]25=a^2+18.9225[/tex]
[tex]a=\pm 2.46526[/tex]
[tex]a\approx\pm 2.5[/tex]
The distance can not be negative, so the length of the apothem is approximately 2.5 cm. Option 4 is correct.
The line OC bisects the angle C.
[tex]tan(30^{\circ})=\frac{a}{b}[/tex]
[tex]\frac{1}{\sqrt{3}=\frac{a}{4.35}[/tex]
[tex]a\approx\pm 2.5[/tex]
Therefore option 2 is correct.
The perimeter of an equality triangle is
[tex]P=3a=3(8.7)=26.1[/tex]
Option 3 is incorrect.
[tex]A=\frac{\sqrt{3}}{4}a^2=\frac{\sqrt{3}}{4}(8.7)^2=32.77[/tex]
Option 5 is incorrect.
Therefore options 1, 2 and 4 are correct.
