Problem solving....algebra?

Question

On Most airlines carry on luggage can have a
Maximum width of 10in. with a maximum volume of 3840 cu. in. If the height of the luggage is2/3 the length, determine the dimensions of the largest piece of carry-on luggage. Use V=lwh...#2Problem:Yield right of way signs used in the US are trinangles. The area of a sign is 558 sq in. The height of the sign is about 5 inches less than its base. Determine the length of the base of a yield right of way sign. Please help solve and explain. The answer to #1 is W=10in. L=24in. H=16in. #2answer is 36in. Do not know how to solve or what formula to use.....help
Its not as easy as it appears...

Answer 1

V=L*w*h
L = length
2/3L=height
v=3840
w=10
substitute in the values and solve for L
3840=L*10*2/3L
384=2/3L^2
384(3/2)=L^2
576=L^2
24=L
Now solve for height
2/3*24=16=height


area of a triangle = 1/2b*h
b = base
b-5 = height
558=1/2*b*(b-5)

1116=b(b-5)
1116=b^2-5b
b^2-5b+1116=0
(b-36)(b+31)
b=36 or -31
can't be -31
so 36
and b-5=31 is the height

Answer 2

#1) Let x= length
then h = 2/3 x height = 2x/3
given w = 10
given that V = lwh = 3840
V=V(x)
V(x) = 10(2x/3)x = 20x^2/3 = 3840
x^2 = 3840(3)/20 = 576
x = sqr[576] = 24

#2) Area of triangle = A = 1/2 base*height
Let base = b
Let height = h = b-5
A = (1/2)(b)(b-5) = (b^2-5b)/2 = 558 or
b^2 -5b - 1116 = 0
b = (--5 +- sqr[(-5)^2 - 4(1)(-1116)])/2(1)
= (5+-sqr[ 4489])/2 = (5+67)/2 = 72/2 = 36

Answer 3

You need to do your own homework, honey.
okay just follow my work here.(X is for Length) 10.x.2/3x=3840
20/3x^2=3840
X^2=3840/(20/3)
X^2=3840*3/20
X^2= 576
(prime factorize 576 to find the square root if you aren't allowed to use a calculator. the factoring is=2.2.2.2.2.2.3.3)
X^2=2.2.2.2.2.2.3.3
X=2.2.2.3
Length=24in
Height=to find height you just have 24*2/3=16 in.

I'm tired of math right now. so sorry i only answered your first question.

Answer 4

study more, we are not here to do your homework. Doing this anyone can be a professional with stolen knowledge. Study, try harder

Answer 5

No snowflake falls in an inappropriate place.