geometry word problem

Question

The length of the base of a triangle is 1 more than twice its height.
The area of the triangle is 18 in2.  What is the length of the base of the triangle?
Please explain the answer and the process involved to reach the solution to this type of problem.

Answer 1

 

Let h = height of triangle

Let 2h+1 = base of triangle ... 1 more than twice the height

 

The formula for the area of a triangle is A = (1/2)• Base • Height

Since the area is 18 in²,

 

     A = (1/2) Base • Height

   18 = (1/2)•(2h+1)•h

   18 = (2h² + h)/2

   2(18) = 2(2h² + h)/2

   36 = 2h² + h

   2h² + h = 36

   2h² + h - 36 = 0

 

Factor

 

   (2h + 9)(h - 4) = 0

 

Using the zero product property

 

   2h + 9 = 0

   2h = -9

   h = -9/2  discard ... we cant have a negative measure

 

    h - 4 = 0

    h = 4

 

The height is 4.  Since the base is 2h + 1,  The base is 2(4)+1 = 8+1 = 9

 

So the height is 4 and the base is 9.

 

CHECK:  1/2 • 9 • 4 = 18

 

Answer 2

Sue, how do we find the area of a triangle? (1/2)bh, right?

 

If the height is h, then the base is 2h + 1. Let's plug it in...

 

18 = (1/2)h(2h + 1)

18 = h² + (1/2)h

2h² + h - 36 = 0

(2h + 9)(h - 4) = 0

 

2h + 9 = 0

       2h = -9

         h = -9/2

Length is never negative, so nope!

 

h - 4 = 0

     h = 4

 

If h = 4, then b = 2(4) + 1 = 9 inches.

 

Hope this helps!