Answer:
the height of the triangle is 6 inches and the base is 7 inches greater, or the base is 13 in
Step-by-step explanation:
The general area-of-a-triangle formula is A = (1/2)(base)(height), or = (1/2)bh.
Here b = h + 7.
Applying the area formula given above: A = 39 in^2 = (1/2)(h + 7)(h), or
78 in^2 = h^2 + 7h,
Rewriting this, in standard quadratic form, we get h^2 + 7h - 78 = 0
-7 ± (49 - 4[1][-78])
Applying the quadratic formula to find h: h = ----------------------------
2
-7 ± (49 + 312) -7 ± 19
or h = ----------------------- = ------------- = {-13, 6}
2 2
Discard the negative 13 root; the height must be a positive quantity.
Thus, the height of the triangle is 6 inches and the base is 7 inches greater, or the base is 13 in
