The height, H, of a triangle is increased by a lenth M, How much must be subtracted from the corresponding base,b, so that the area of the new triangle is one-half that of the original triangle.
I think the main difficulty with this problem is sorting out the English and putting it in mathematical terms. The area of a triangle is one half the base times the height. You are starting with a triangle of height H and base b so its area is
You now increase the heigh by M to H + M and decreaes its base by S to b - S so the area of the transformed triangle is
The area of this transformed triangle is to be one half the area of the original triangle so
Now solve for S.