Answer:
the triangle
Step-by-step explanation:
The perimeter is the sum of the all sides of the shape.
Triangle:
3√147+2√108+2√48+3√75+ 6√12
147=49•3, 108=36•3, 48=16•3, 75=25•3, 12=4•3 that means
√147=7√3, √108=6√3, √48=4√3, √75=5√3, √12=2√3
perimeter=3•7√3+2•6√3+2•4 √3+3•5√3+6•2√3=68√3
Square:
4•1/3•√63=4/3•√9•√7=4√7
Rectangle:
2•1/4√100+2(2√48+4√75)=
5+2(8√3+20√3)=5+56√3
Now, if you use a calculator, you will find that the greatest perimeter is for the triangle shape.
Answer:
answer is option A
A, 4+12>6✓
12+6>4✓
4+6>12×
because sum of two sides lengths ina a triangle should greater than the other side's length
Answer:
tan(2u)=[4sqrt(21)]/[17]
Step-by-step explanation:
Let u=arcsin(0.4)
tan(2u)=sin(2u)/cos(2u)
tan(2u)=[2sin(u)cos(u)]/[cos^2(u)-sin^2(u)]
If u=arcsin(0.4), then sin(u)=0.4
By the Pythagorean Identity, cos^2(u)+sin^2(u)=1, we have cos^2(u)=1-sin^2(u)=1-(0.4)^2=1-0.16=0.84.
This also implies cos(u)=sqrt(0.84) since cosine is positive.
Plug in values:
tan(2u)=[2(0.4)(sqrt(0.84)]/[0.84-0.16]
tan(2u)=[2(0.4)(sqrt(0.84)]/[0.68]
tan(2u)=[(0.4)(sqrt(0.84)]/[0.34]
tan(2u)=[(40)(sqrt(0.84)]/[34]
tan(2u)=[(20)(sqrt(0.84)]/[17]
Note:
0.84=0.04(21)
So the principal square root of 0.04 is 0.2
Sqrt(0.84)=0.2sqrt(21).
tan(2u)=[(20)(0.2)(sqrt(21)]/[17]
tan(2u)=[(20)(2)sqrt(21)]/[170]
tan(2u)=[(2)(2)sqrt(21)]/[17]
tan(2u)=[4sqrt(21)]/[17]
