1. The area of a rhombus measures $120 \mathrm{~cm}^{2}$. The difference in the lengths of its diagonals is $14 \mathrm{~cm}$. What is the length of the side of the rhombus?
1. Considering the reasonable relationship between the diagonals $e-f=14$ or $e=14+f$. We use the formula for the area of a rhombus $\frac{e \cdot f}{2}=120$. Substitute $e$ and we get the quadratic equation $f^{2}+14 f-240=0$. Solve the equation. We get the solutions $f_{1}=10$ and $f_{2}=-24$, which is not valid. The length of the side $a$ is calculated using the Pythagorean theorem $a^{2}=\left(\frac{e}{2}\right)^{2}+\left(\frac{f}{2}\right)^{2}$. We calculate $a=13$.

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Using the formula for the area of a rhombus ...................................................................................................

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