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.

Hello from MrBillDoesMath!

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

b. x + 1

step-by-step explanation:

i'am smart

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol