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.

Hi Wilder,

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.

Cheers,
Penny