# A rectangle is constructed with it's base on the x-axis and the two of its vertices on the parabola #y=49 - x^2#. What are the dimensions of the rectangle with the maximum area?

##### 1 Answer

In other words, we're constructing a rectangle under a dome-shaped form.

#### Explanation:

The parabola is a 'mountain'-type (because the coefficient of

We can now simplify the problem to finding a rectangle with vertices at

The area will then be

If we substitute the equation of the parabola for

To find the extremes (max of min) we need the derivative and set it to zero:

(remember we will have to double that)

Use this in the original function:

**Answer** :

Dimensions will be

graph{49-x^2 [-65.4, 66.33, -13.54, 52.3]}