Question

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

Answer 1

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

Explanation:

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

`A = (1)/(2)\cdot n \cdot (n+1)`

`A = (1)/(2)\cdot (n^(2)+n)`

`A = (n^(2))/(2)+(n)/(2)`

`n^(2)+n = 2\cdot A`

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

And we get the following second-order polynomial:

`n^(2)+n -2\cdot A = 0` (1)

If we know that
`A = 17.5\,cm^(2)`, then the shortest length of the triangle is:

`n_(1) = 5.437\,cm` and
`n_(2) \approx -6.437\,cm`

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

`n\approx 5.437\,cm`

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