"Published in Vacaville, California, USA"
A parcel of land is 6 ft longer than it is wide. Each diagonal from one corner to the opposite corner is 174 ft long. What are the dimensions of the parcel?
Solution:
To illustrate the problem, it is better to draw the figure as follows
 |
| Photo by Math Principles in Everyday Life |
Since the two diagonals of a parcel are equal, then the parcel is a rectangle in which all sides are perpendicular to each other. If the diagonal is given, then we can solve for the width of a rectangle by Pythagorean Theorem as follows
By completing the square method,
Since the dimensions of a rectangle are all positive values, then we have to choose the positive sign. Hence, the width of a rectangle is
and the length of a rectangle is
.Therefore, the dimensions of a parcel of land are 120 ft by 126 ft.