Question

The base of a triangle is twelve more than twice its height. If the area of the triangle is 42 square centimeters, find its base and height.

Answer 1

Hello from MrBillDoesMath!

Answer:

h =  ( -6 + sqrt(204) ) / 2

b =   6 + sqrt(204)

Discussion:

Area of a triangle = (1/2) b h

where "b" is the length of the base and "h" is the height of the altitude.

We are told that

A = (1/2) * (2h +12)* h  and

A = 42.

Equating both sides gives

(1/2) (2h+12)*h = 42.

Multiplying both terms in the left side by (1/2) gives:

(  (1/2) 2h + (1/2) 12) ) * h = 42  or

(h + 6) * h = 42 or

h^2 + 6h = 42.  Subtract 42 from both sides:

h^2 + 6h - 42 = 0.

Using the quadratic formula:

h = ( -6 + sqrt( 6^2 - 4(1)(-42) )    / 2(1) =

     ( -6 + sqrt (36+ 168) )   / 2             =

     ( -6 + sqrt(204) ) / 2

Not a nice number.

Base = 2h + 12 =  

    { ( -6 + sqrt(204) ) /2  }  * 2     + 12  =

    (-6 + sqrt(204)) + 12  =

     6 + sqrt(204)

Thank you,

MrB