Height of a triangle with base 5m and area 20m2

Since the "base of a triangular sail is 5m shorter than its height", we have the equality  

 Start with the formula for the area of a triangle 

 Plug in , , and  

 Multiply both sides by 2 

 Distribute 

 Subtract 36 from both sides 

 Factor the right side (note: if you need help with factoring, check out this solver) 

Now set each factor equal to zero: 
 or  

 or  Now solve for x in each case 

So our possible answers are 

 or  

However, since a negative height doesn't make sense, our only solution is  

So the height is 9 m 

Now subtract 5 from the height to get the base 

 

So the base is 4 m 

Check: 

 Start with the formula for the area of a triangle 

 Plug in , , and  

 Multiply 

 Divide. Since the two sides of the equation are equal, this verifies our answer. 

If you have a triangle with a base of 5m and an area of 20m2, to find the height begin with the formula of the area of a triangle.

A=1/2bh

Then, plug in your known numbers

20m2=1/2h(5m)

What I do next, is I work backwards by dividing the are by 1/2, which equals 40. All that is left to do, is divide this number, 40, by 5 to find the height.

40/5=8

Therefore, the height of the triangle is 8m

A. x3 - 5x2 + 3x - 54