## Saturday, December 27, 2014

### Square, Rectangle, and Parallelogram Problems, 14

Category: Plane Geometry

"Published in Vacaville, California, USA"

A rectangular parcel of land has an area of 5000 ft². A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, correct to the nearest foot?

 Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above

 Photo by Math Principles in Everyday Life

If a rectangle is cut by its diagonal, then the resulting figure is a pair of right triangles. By Pythagorean Theorem, the width of a rectangle is

Hence, the area of a rectangle is

Square on both sides of the equation, we have

Since the resulting equation cannot be factored by synthetic division, factoring, grouping, or substitution method, then we have to do the trial and error method by assigning the values of x until the left side of the equation equals the right side of the equation which is zero as follows

 Photo by Math Principles in Everyday Life

It is better to do the calculations if you will use Microsoft Excel because you can put the formula like for instance, the resulting cubic equation that we can't factor by any method. You can enter any values of x and the Excel program will give us the result as shown at the table above.

From the result as shown at the table above, we have to choose the value of x which is 106.0805885 because the result is closer to zero. Hence, the length of a rectangle is 106.0805885 ft ≈ 106 ft.

The width of a rectangle is

Therefore, the dimensions of the rectangular land are 106 ft by 47 ft