Area of a Right Angle: find cost of new mainsail for boat

[jlaw]

Hi Algebra Experts!

Could someone please have a look at this and tell me if it's right?

Problem: The mainsail on a sailboat is a right triangle in which the hypotenuse is called the leech. A 12-foot tall mainsail has a leech of 13 feet. If sailcloth costs $10.00 per square foot, what is the cost of a new mainsail?

x^2 + 12^2 = 13^2
x^2 + 144 = 169
x^2 - 25 = 0
(x-5) (x+5)
x = 5
= 5^2 + 12^2 = 13^2 The measurements of the sail (right triangle)

Formula for the area of a triangle is S= (1)/2 *b*h

S = (1)/2 * 5 * 12
S = 30
Area is 30 sq ft * 10 (dollars per sq foot) = $300 dollars for a new main sail.

What do you think? It seems right but the text did not give us the formula for the area of a triangle. I found that formula on the internet. :?

Grateful,
Julia

 

[tkhunny]

Re: Area of a Right Angle

Not bad, but you have overlooked one important thing - practicality.

1) can you find uncut fabric in that size? If not, you'll have to stitch it together. This will take more fabric.

2) Are you planning to attach it by magic? My guess is you'll have to double up on the edges, all the way around. This will take more fabric.

Good work!

 

[Deleted member 4993]

Re: Area of a Right Angle

Like tkhunny explained, that is your minimum cost. As long as you attach that adjective (minimum) to your answer - you get flying colors ( oh that I suppose is aerospace term - not marine).

 

[jlaw]

Like tkhunny explained, that is your minimum cost. As long as you attach that adjective (minimum) to your answer - you get flying colors ( oh that I suppose is aerospace term - not marine).

Thank you Subhotosh Khan!! Honestly, I still wasn't certain if I had it right till I saw you post. Much gratitude for your posting.

Sincerely,
Julia

 

[jlaw]

Re: Area of a Right Angle

Not bad, but you have overlooked one important thing - practicality.

1) can you find uncut fabric in that size? If not, you'll have to stitch it together. This will take more fabric.

2) Are you planning to attach it by magic? My guess is you'll have to double up on the edges, all the way around. This will take more fabric.

Good work!

Thank you for your response Tkhunny. The first sentence, made me wonder if it the work was wrong but I think you were saying that it's okay.

Being an advid artist, I've sewed and done some upholstery work. You're right though, fabrics don't come in that size and if it were to be done in stripes or have any pattern in it I would certainly need more than 30 sq ft to match up patterns or lines. However, I would not take on creating something as life preserving as a main sail. Hopefully, anyone wanting a new main sail could turn in the size to an expert who could manage to cut and stitch the fabric together. For them do it, my hands never touching any of it, I just may consider that magic just like a friend I know claims that internet powers are magical...and she calls some of the gagets "That Starwars thing that you plug into the computer" ..giggles.

The knowledge you all have seems like magic to me=the unknowing and sometimes lost. :wink:

Gratitudes for Your much need feedback.
Sincerely,
Julia