A sail is in the form of a right triangle that is four times as high as it is wide. The sail is made from 18 square meters of material. What is its height?

Question

This is solved by using the Quadratic equation but i have no clue how to.

Answer 1

Hi Randal,

 

We can use the formula for area of a triangle to solve this problem

 

A = (1/2)ab             where a is the altitude or height and b is the base     also we know that a = 4b in this problem

 

and we know that A = 18 sq ft

 

so

 

18 = (1/2)(4b)b

 

18 = 2b²

 

9 = b²

 

b = 3                   so the base is 3

 

and the height is 4 times that

 

a = 4(3) = 12              (height of the sail

 

Hope this helps

Answer 2

Start with the area of a triangle:

 

A = (1/2)*base*height

 

Let w = the base (width) and h = the height.  The triangle is 4 times as high as it is wide; that is h = 4w.  So substitute 4w in place of h in the area equation:

 

A = (1/2)*w*4w = 2w²

18 = 2w²

9 = w²

√9 = √w²

 

±3 = w

 

Since we can't have a length of -3, w = 3 and h = 4w = 12

 

Check

Area = (1/2)*w*h

18 = (1/2)*3*12

18 = (1/2)*36

18 = 18

Check!