Mary thinks the triangle is equilateral. how would you support or dispute her conjecture?

Mathematics

1 answer:

timurjin [86]3 years ago

6 0

Answer:

Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.

Step-by-step explanation:

An equilateral triangle would have three sides that are all the same length, out of these options, only using the distance formula to calculate the length of all three sides and checking whether they are all congruent will make sure that the triangle is equilateral instead of just isosceles.

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The formula of the area of the equilateral triangle:
$A_\Delta=\dfrac{a^2\sqrt3}{4}\\\\a=3\to A_\Delta=\dfrac{3^2\sqrt3}{4}=\dfrac{9\sqrt3}{4}$

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$T.A.=2A_\Delta+3A\\\\T.A.=2\cdot\dfrac{9\sqrt3}{4}+3\cdot18=\dfrac{9\sqrt3}{2}+54=(54+4.5\sqrt3)\ in^2$
The formula of the volume of the triangular prism:
$V=A_\Delta\cdot l\\\\V=\dfrac{9\sqrt3}{4}\cdot6=\dfrac{9\sqrt3}{2}\cdot3=\dfrac{27\sqrt3}{2}=13.5\sqrt3\ in^3$

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