SOLUTION: would you please help me with this problem, i have been racking my brain for two days to figure it out...ok this is how it goes: There is a sailboat which must have a 110 ft mast a

Question 185893This question is from textbook Beginning Algebra
: would you please help me with this problem, i have been racking my brain for two days to figure it out...ok this is how it goes: There is a sailboat which must have a 110 ft mast and a combined mainsain and jibsail area of 3000 sq ft. The design calls for the mainsail to be 60% of the combined sail area,and the jibsail area to be 40%(of course). If the height of the triangular mainsail is 28ft more than twice the length of the boom, find the length of the boom and the height of the mainsail.
I've figured out this much so far... the mainsail=1800sq ft, and the jibsail =1200sq ft. Height=(2(boom)+28sq ft). and i know that the area of a triangle is A=1/2(base)(heigth). that is about it, i've played around with the numbers but haven't gotten it correct yet. Any help you can offer would be tramendous!Thanks This question is from textbook Beginning Algebra

Found 2 solutions by scott8148, ankor@dixie-net.com:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
you do know that the boom is the base, right?

1800 = 1/2 * boom * (2(boom)+28)

1800 = b^2+14b ___ 0 = b^2+14b-1800

factoring ___ 0 = (b-36)(b+50)

so b=36

and h=100
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
There is a sailboat which must have a 110 ft mast and a combined mainsail and jib-sail area of 3000 sq ft. The design calls for the mainsail to be 60% of the combined sail area,and the jib-sail area to be 40%(of course). If the height of the triangular mainsail is 28ft more than twice the length of the boom, find the length of the boom and the height of the mainsail.
:
We can determine that the mainsail area must be .6*3000 = 1800 sq/ft
:
Assume the mailsail is a right triangle,
let x = the length of the boom\
then
(2x+28) = the height of the mainsail
we have the area equation:
.5 * x * (2x+28) = 1800
.5x(2x+28) = 1800
1x^2 + 14x = 1800
a quadratic equation:
x^2 + 14x - 1800 = 0
Factor this to
(x+50)(x-36) = 0
positive solution:
x = 36' is the boom
and the height of the mainsail
2(36) + 28 = 100'
;
:
Check the area:
.5*36*100 = 1800 sq/ft

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