Answer:
base = 8 in; height = 3 in
Explanation:
Let h stand for the height of the triangle. Then 2h+2 will be the base length, and the area is ...
A = 1/2bh
12 = 1/2(2h+2)(h) = (h+1)(h)
We know that factors of 12 that differ by 1 are 4 and 3, so we conclude ...
h = 3
2h+2 = 8
Both dimensions are in inches.
_____
Comment on the solution
If you work through the solution of the quadratic, you find solutions are ...
h = -4, h = 3
That is, the pairs (-4, -3) and (3, 4) are both pairs of (h, h+1) that have a product of 12.
The negative solution is extraneous.