the height of a triangle is 21 less inches than 4 times the base. The area is 9 square inches. Find the length of the base and the height of the triangle

Question

I really do not know how to do this problem. I believe something is squared I just do not know what.

Answer 1

Hi Kristian,

 

The area of a triangle is

 

A = (1/2)bh

 

Where b is the base and h is the height.

 

We are told that the height is 21 less than 4 times the base. Mathematically, this is expressed as 

 

h = 4b - 21

 

We are also told that the area is 9 square inches. So, 

 

A = 9

 

So, we have basically two equations:

 

(1/2)bh = 9

 

h = 4b - 21

 

We want to eventually find b and h.

 

Let's substitute the second equation into the first, eliminating h:

 

(1/2)b(4b - 21) = 9

 

Multiply both sides of this equation by 2.

 

b(4b - 21) = 18

 

4b^2 - 21b - 18 = 0

 

(4b + 3)(b - 6) = 0

 

So, 4b + 3 = 0

 

or

 

b = -3/4

 

And,

 

b = 6

 

Since we are dealing with lengths, we can discard the negative answer as unphysical. So, the base is b = 6 in.

 

We can pick either of the original equations to solve for h now than we know b. I pick the area equation:

 

(1/2)bh = 9

 

or 

 

bh = 18

 

Or

 

h = 18/b

 

Or 

 

h = 18/6

 

or 

 

h= 3

 

base = 6 in, height = 3 in