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A. Which statements about finding the area of the equilateral triangle are true? Check all that apply.


B. The apothem can be found using the Pythagorean theorem.


C. The apothem can be found using the tangent ratio.


D. The perimeter of the equilateral triangle is 15 cm.


E. The length of the apothem is approximately 2.5 cm.


F. The area of the equilateral triangle is approximately 65 cm2.

A Which statements about finding the area of the equilateral triangle are true Check all that apply B The apothem can be found using the Pythagorean theorem C T class=

Respuesta :

calculista

Statements

case 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

[tex] b=\frac{8.7}{2} =4.35\ cm [/tex]

Applying the Pythagorean Theorem

[tex] 5^{2} =a^{2} +b^{2} \\ a^{2}=5^{2} -b^{2} \\ a^{2}=5^{2} -4.35^{2}\\ a^{2} =\sqrt{6.0775\\}\\\\ a=2.47\ cm [/tex]

[tex] a=2.5\ cm [/tex]

case 2) The apothem can be found using the tangent ratio

The statement is True

we know that

[tex] tan\ 30=\frac{a}{b} \\ \\ a=b*tan\ 30\\ \\ a=4.35*\frac{\sqrt{3}}{3} \\ \\ a=2.51\ cm [/tex]

[tex] a=2.5\ cm [/tex]

case 3) The perimeter of the equilateral triangle is 15 cm

The statement is False

we know that

perimeter of the equilateral triangle is equal to

[tex] P=8.7*3=26.1\ cm [/tex]

case 4) The length of the apothem is approximately 2.5 cm

The statement is True

see case 1) and case 2)

case 5) The area of the equilateral triangle is approximately 65 cm2

The statement is False

Applying the law of sines

[tex] A=\frac{1}{2} *8.7*8.7*sin\ 60 \\ \\ A=32.77\ cm^{2} [/tex]

therefore

the answer is

case 1) The apothem can be found using the Pythagorean theorem

case 2) The apothem can be found using the tangent ratio

case 4) The length of the apothem is approximately 2.5 cm

Ver imagen calculista

The statements true equilateral triangle are apothem found using the Pythagorean theorem and tangent ratio. The length of the apothem is 2.5 cm.

What is Pythagoras theorem?

Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of the square of other two legs of right angle triangle.

In the given figure, the side of the equilateral triangle is 8.7 cm. The length of the side b is half of the side of the triangle. Thus,

[tex]b=\dfrac{8.7}{2}\\b=4.35[/tex]

The length which is marked with 5 cm is the hypotenuse side in a small right angle triangle and a,b are other sides. Thus, by the theorem of Pythagoras,

[tex]a^2+b^2=5^2\\a^2+(4.35)^2=25\\a=\sqrt{25-4.35^2}\\a=2.5[/tex]

The length of apothem can be found out using the tangent ratio as,

[tex]\tan30=\dfrac{a}{4.35}\\a=(\tan30)\times4.35\\a\approx2.5\rm\;cm[/tex]

Thus, the length of the apothem is approximately 2.5 cm.

In the given figure, the side of the equilateral triangle is 8.7 cm. Thus, the area of this triangle is,

[tex]A=\dfrac{\sqrt3}{4}8.7^2\\A\approx32.77\rm\; cm^2[/tex]

The perimeter of the triangle is,

[tex]P=3\times8.7\\P=26.1\rm\; cm[/tex]

The statements true equilateral triangle are apothem found using the Pythagorean theorem and tangent ratio. The length of the apothem is 2.5 cm.

Learn more about the Pythagoras theorem here;

https://brainly.com/question/343682

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