Question 185893
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