The base of a triangular sail is 13 m shorter than its height. The area is 84 m squared. Find the base and height of the sail.?

Let b be the base and h be the height.

Area of a triangle is given by A = (1/2)bh

The given information says that

b = h - 13

The given information about the area translates to

(1/2)bh = 84

Plug in (h - 13) for b in that equation and solve for h :

(1/2)(h - 13)h = 84

(h - 13)h = 168 . . . . . . . . . . multiplied both sides by 2

h² - 13h = 168 . . . . . . . . . . . multiplied out left side

h² - 13h - 168 = 0 . . . . . . . . subtracted 168 from both sides

(h + 8)(h - 21) = 0 . . . . . . . . factored left side

By the principal of zero products, the solutions are h = -8 and h = 21 .

Discard the negative solution since negative height is meaningless.

Plug h = 21 into the equation for b at the top :

b = h - 13 = 21 - 13 = 8

base is 8 m

height is 21 m