College Algebra word problem?

Let b = the length of the base, and b - 2 = the height.

A = (1/2)bh = (1/2)b(b - 2) = 17.5

b(b - 2) = 35

b^2 - 2b = 35

b^2 - 2b - 35 = 0

(b - 7)(b + 5) = 0

b = 7 or b = -5 (reject)

The base is 7 cm.

Ok, this word problem gives describes a triangle by giving you two relations. Lets start by calling the height of the triangle a number h, and the base a number b. The first sentence tell you that:

h = b - 2

The second relation is not as obvious. However, you can relate the area of a triangle to its base and height through the formula:

A = 0.5 * b * h

but we know from the first relationship what h is in terms of b, so we can just plug that in to the formula for area along with the actual area given in the problem:

17.5 = 0.5 * b * (b - 2)

Solving this is pretty simple. First divide both sides by 0.5:

35 = b* (b-2)

then expand:

35 = b^2 - 2b

next, move everything to one side and factor:

b^2 - 2b - 35 = 0

(b - 7)(b + 5) = 0

Solving gives either 7 or -5 units length. However, -5 doesn't make sense when talking about lengths of sides of triangles, so we can throw this one out.

Note: formula for the area of a triangle is .5 * b * h (b = length of base, h = length of height)

So, we know that

(b * h)/2 = 17.5

we also know that

b - 2 = h (think about it this way, if the base is 13 cm, and we know the height is 2 cm less than 13, then our height is 11. So height = base - 2).

Thus we have a system of equations

(.5)bh = 17.5

h = b - 2

You should be able to solve it from there.

x(x-2)=35