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
