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

$A = \frac{1}{2}bh$

Substituting the values of Area, base and height,

$30 = \frac{1}{2}x(x+7)$

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.