Question

Help please I'm on a huge time crunch!!! I will fan and medal the most helpful person!!!!!!!

Answer 1

What is the value of b in the triangle shown above?
A.) -4inches
B.) 4inches
C.) negative or positive 4inches
D.) no solution

Answer 2

Is the "24in. sq." pertaining to the area? or to that third side?

Answer 3

the 3rd side

Answer 4

hmmm... i dont think its the 3rd side..
if it is the third side then u can use pythagoras theorem \[(AC) ^{2} = (AB)^{2} + (BC)^{2}\]\[24^{2} = (3b)^{2} + b^{2}\]\[24^{2} = 10b^{2}\]and
obviously the answer is not given.. but its not the "no solution " since there is an value for "b" when u solve the above expression.. so the (24) .in. sq should be the area

Answer 5

then that would be
c^2 = a^2 + b^2
24^2 = 3b^2 + b^2
576 = 4b^2 All divided by 4
144 = b^2
\[\sqrt{144} = \sqrt{b ^{2}}\]
12 = b

Answer 6

My answer comes with the pythagorean theorem, assuming it IS the 3rd side. if not, follow his answer^^^^^^

Answer 7

so...
\[Area \ of \ a \ \triangle =\frac{ base \times height }{ 2 }\]\[= \frac{ AB \times BC }{ 2 }\]\[= \frac{ 3b \times b }{ 2 }\]
since the area is 24 sq.in
\[24 = \frac{ 3b \times b }{ 2 }\]\[48 = 3b \times b\]\[48 = 3b^{2}\]\[b^{2} = \frac{ 48 }{ 3 } = 16\]\[b = \pm \sqrt{16}\]which means
\[b = +4 \ or \ -4\]
but a length of a side of a triangle is always positive which means
b = 4

Answer 8

got it :) ?

OH! and btw ECSarabia u have done some miscalculations in ur simplifications... i think u should check it twice :)

Answer 9

Yes I got it thanks a bunch!!!

Answer 10

oh thanks. i've been a little off my game today. I think i'll stop "helping" because i have some stuff on my mind. Clouding my Arithmatic reasoning right now.

Answer 11

it's okay to take a break every once in a while