Let h represent the height. Then the base is h+6 (all measurements are in feet).
The formula for the area of a triangle is A = (base)(height)/2.
Here A = 114 ft^2 = (base)(height)/2. Substituting the (h+6) and h,
A = [114 ft^2] = [(h+6)(h)]/2 , or [h^2 + 6h]/2, or 2A = 228 = (h+6)h. Multiply out the right side
Solve 228 = h^2 + 6h for h:
h^2 + 6h - 228 = 0
Applying the Quadratic Formula,
-6 plus or minus sqrt(36-4(1)(-228))
h = -------------------------------------------------
2
-6 plus or minus sqrt(948) -6 plus or minus 30.79
or h = ------------------------------------- = ------------------------------------ 2 2
-6 plus or minus 30.79
h = ----------------------------------
2
We want only the positive result. That comes to h = 30.79-6
----------
2
or 24.79/2, or h = 12. 40
h represents the altitude of the triangle, so h+7 represents the length of the base. These values are 12.40 feet and 19.40 feet respectively.
Substitute b=19.40 feet and h=12.40 feet into the formula A = bh/2.
Is the result 114 sq. ft. ?
