Let the base be b. The the height of the triangle is b+2.
(base)(height)
The area of any triangle is A = ----------------------
2
(b)(b+2)
Here, A = 20 cm^2 = --------------
2
so 40 cm^2 = b^2 + 2b, or b^2 + 2b - 40 = 0
solving this quadratic with the quadratic formula:
-2 plus or minus sqrt( 4-4(1)(-40) )
b = --------------------------------------------------
2
= -1 plus or minus sqrt( 4 + 160) = -1 plus or minus sqrt 164
Note that sqrt(164) = sqrt(4)sqrt(41) = 2sqrt(41)
so b = -1 plus or minus 2sqrt(41). We must eliminate the negative root here. So, we get b = -1 + sqrt(41). Then the height is h = -1 + 2 + sqrt(41), or
b = -1 + sqrt(41) and h = b+2 = 1 + sqrt(41) (answer)
