Find the dimensions of the sail

Question

The sail on a sail boat is in the shape of a triangle. If the height of the sail is 3 times the length of base and the area is 54 square feet, find the dimensions of the sail.

Answer 1

The Area of a triangle is equal to 1/2 bh: A = 1/2bh. If we plug into the equation the information given, letting b = base, we get: 54 sq.ft. = 1/2b(3b). Multiplying both sides of the equation by 2 we get

108 sq.ft. = 3b². dividing both sides of the equation by 3 we get 36 sq.ft. = b². Taking the square root of both sides of the equation gives us 6 ft. = b. That means that the height of the sail is 3b = 18 ft. Now to find the dimension of the third side of the sail. Assuming the sail is a right triangle, we can use Pythagorus' Theory: A² + B² = C², where C = length of the hypotenuse. Our equation becomes 6² + 18² = C². This becomes 36 + 324 = C². 360 = C^2, √C² = √360, C = 18.97 ft. So, the answer to the question, the dimensions of the sail are base = 6 ft, height = 18 ft, and hypotenuse (long side of the sail) is 19 ft.

Answer 2

The area of a triangle is 1/2 base times height. Since they tell you the area is 54, your formula should be the following:

54 = 1/2 x b x h

Your base is b and your height you are told is 3 x b so,

54 = 1/2 x b x 3b

54 = 1/2 x 3b^2

Multiply both sides by 2 in order to cancel out the fraction

2(54) = 2(1/2) x 3b^3

108 = 3b^2

Divide both sides by 3 In order to isolate your variable

108/3 = 3b^2

36 = b^2

Square root both sides would like to find b

b = 6

Remember that your height is equal to 3 x b = 3 x 6 = 18

So your base = 6 and your height = 18

You can check your answer is correct by doing :

1/2 x b x h

1/2 x 6 x 18 which does = 54

Answer 3

Let x = the width

then 3x = the height

The area = .5(base)(height) = .5(x)(3x) = (3/2)x² = 54

So,

x² = 36 or x = 6

Therefore,

Width = 6

Height = 18