Question

A sailboat has a triangular sail with an area of 30 square feet. the height of the sail is 7 feet more than the length of the base of the sail. find the height of the sail.

Answer 1

It is given in the question that,

A sailboat has a triangular sail with an area of 30 square feet. the height of the sail is 7 feet more than the length of the base of the sail.

Let the length of the base be x, so height is

`(x-7)feet`

And formula of area of triangle is

`A = (1)/(2)bh`

Substituting the values of Area, base and height,

`30 = (1)/(2)x(x+7)`

Multiplying both sides by 2

`60 = x^2 + 7x`

`x^2+ 7x-60=0 \\ (x+12)(x-5)=0 \\ x=5 feet`

So the base is 5 feet and the height is 12 feet.