<span>Given cotA + cotB + cotC = sqrt3
to prove triangle ABC is equilateral
we prove this by assuming ABC to be equialteral and establishing the truth
of the statement cotA + cotB + cotC =sqrt3
since ABC is equialteral angleA=angleB=angleC=60 degrees
cotA=cotB=CotC = cot60= 1/sqrt3
therefore cotA + cotB + cotC = 1/sqrt3 + 1/sqrt3 + 1/sqrt3
=3/sqrt3
=sqrt3 which is equal to the RHS ( right hand side) of the expression
hence our assumption that ABC is equilateral is true</span>
My teacher told me that I means fraction pie
If we consider "a" as the edge length, and "D" the cube's diagonal, we have that the square cube's diagonal is equal to the edge length's square plus the side diagonal (d) square (Pythagoras theorem)
a² + d² = D²
And since:
d² = a² + a²
Clearing a, we have:
a² = D²-d²
<span>a² = D²-2a²
</span><span>3a² = D²
</span>
a = √(<span>
D²/3)</span>
Surface area is equal to 6·a², so the surface area will be 6·(D²/3) =
2D²The volume is a³, so the volume will be √(D²/3)³ = √
(<span>/3</span>³<span>) =
D</span>
³/√27
The area of two yards is 18ft