SOLUTION: Which statements about finding the area of the equilateral triangle are true? Check all that apply. https://media.edgenuity.com/evresources/8101/8101-10/8101-10-04/8101-10-04-asse

Algebra ->  Polygons -> SOLUTION: Which statements about finding the area of the equilateral triangle are true? Check all that apply. https://media.edgenuity.com/evresources/8101/8101-10/8101-10-04/8101-10-04-asse      Log On


   

Question 1131625: Which statements about finding the area of the equilateral triangle are true? Check all that apply.
https://media.edgenuity.com/evresources/8101/8101-10/8101-10-04/8101-10-04-assessment/8101-10-04-23-image1.PNG
The apothem can be found using the Pythagorean theorem.
The apothem can be found using the tangent ratio.
The perimeter of the equilateral triangle is 15 cm.
The length of the apothem is approximately 2.5 cm.
The area of the equilateral triangle is approximately 65 cm2.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1. The apothem can be found using the Pythagorean theorem->The statement is True
we know that
If ABC is an equilateral triangle (see the attached figure with letters to better understand the problem)
then
AB=BC=AC
b=8.7%2F2+=4.35 cm
Applying the Pythagorean Theorem
5%5E2+=a%5E2+%2Bb%5E2+
a%5E2=5%5E2+-b%5E2
a%5E2=25+-4.35%5E2
a%5E2+=sqrt%286.0775%29+
a=2.47 cm
a=2.5 cm


2.The apothem can be found using the tangent ratio->The statement is True
we know that
tan%2830%29=a%2Fb
a=b%2Atan%2830%29
a=4.35%2Asqrt%283%29%2F3++
a=2.5 cm


3. The perimeter of the equilateral triangle is 15cm ->The statement is False
we know that perimeter of the equilateral triangle is equal to
P=8.7%2A3=26.1cm


4. The length of the apothem is approximately 2.5 cm ->The statement is True
see 1. and 2.


5. The area of the equilateral triangle is approximately 65cm%5E2->The statement is False
Applying the law of sines
A=%281%2F2%29+%2A8.7%2A8.7%2Asin%28+60%29+
A=32.77+cm%5E2


therefore
the answer is:
The apothem can be found using the Pythagorean theorem
The apothem can be found using the tangent ratio
The length of the apothem is approximately 2.5cm