Two sides of a triangle are two consecutive number, whose area is 17.5cm². Find the numbers

The numbers associated with the triangle are 5.437 and 6.437 centimeters, respectively.

Step-by-step explanation:

Two numbers are consecutives, when their difference is equal to 1. The area of the triangle is determined by the following formula:

Where is the shortest length of the triangle, measured in centimeters.

And we get the following second-order polynomial:

(1)

If we know that , then the shortest length of the triangle is:

and

Since length is a positive variable, the only possible solution is:

Then, the numbers associated with the triangle are 5.437 and 6.437 centimeters, respectively.