Question

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

Answer 1

Answer:

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:

$A = \frac{1}{2}\cdot n \cdot (n+1)$

$A = \frac{1}{2}\cdot (n^{2}+n)$

$A = \frac{n^{2}}{2}+\frac{n}{2}$

$n^{2}+n = 2\cdot A$

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.