Question

The height of the sail on a boat is 7 feet less than 3 times the length of its base. If the

The area of the sail is 68 square feet, find its height and the length of the base.

Answer 1

Base=8 feet

Height=17 feet

Explanation:

Let

Base=x

Height=3x-7

Area=68 square feet

Area of the sail boat=1/2 * base * height

68 = 1/2 * x * (3x-7)

Cross product

68 * 2 =(1) * (x) * (3x-7)

136 = 3x^2 - 7x

3x^2 - 7x - 136=0

Using quadratic formula

x= -b +or- √b^2 - 4ac / 2a

= -(-7) +or- √(-7)^2 - (4)(3)(-136) / 2(3)

= 7 +or- √49 - (-1632) / 6

= 7 +or- √49+1632) / 6

= 7 +or- √1681 / 6

=7 +or- 41 /6

x= 7+41 / 6 or 7-41 / 6

=48/6 or -34/6

=8 or -17/3

Answer:

Explanation:

Let

Base=x

Height=3x-7

Area=68 square feet

Area of the sail boat=1/2 * base * height

68 = 1/2 * x * (3x-7)

Cross product

68 * 2 =(1) * (x) * (3x-7)

136 = 3x^2 - 7x

3x^2 - 7x - 136=0

Base of the boat can't be a negative value

Therefore,

Base = x = 8 feet

Height= 3x-7

=3(8)-7

=24-7

=17 feet