Suppose that the area of a trapezoid can be represented by the expression 35/x square feet and lengths of the parallel bases of the trapezoid can be represented by the expressions

Question

Suppose that the area of a trapezoid can be represented by the expression 35/x square feet and lengths of the parallel bases of the trapezoid can be represented by the expressions a=2/x feet and b=8/x+1 feet respectively. If the height is 10 feet determine the value of x . Then determine the area and values of the lengths of the parallel bases

Answer 1

Well, this is a bad problem, but let's walk it through. We can use the formula for the area of a trapezoid to solve for what the questions asks.

A = h * (a+b)/2

We are given h and we know A, a, and b are all in terms of one variable, x

Since we have one variable and one equation, we can solve the problem. Let's substitute all our quantities into the area equation like so:

35/x = 10 * (2/x + 8/x + 1)/2

Simplifying the right-hand side a little, we get:

35/x = 5 * (10/x + 1)

And a little more:

35/x = 50/x + 5

Now, If we multiply both sides by x, we get:

35 = 50 + 5x

Finally, if we subtract 50 from both sides and divide by 5, we get:

x = -3

And that's bad because no geometry can have a negative value. I would tell your teacher to revise it so that the area is at least 60/x.

If anyone finds an error in my work, please point it out.