Free space in the garden

The grandfather's free space in the garden was in the shape of a rectangular triangle of 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. The smaller part creates a rock garden, for the larger sows grass. How many square meters has a larger part?

Correct answer:

S =  25.5621 m²

Step-by-step explanation:

$$\begin{gathered} a=5\text{m} \\ b=12\text{m} \\ c=\sqrt{a^2+b^2}=\sqrt{5^2+12^2}=13 \\ {S}_1=\frac{a\cdot b}{2}=\frac{5\cdot 12}{2}=30{\text{m}}^2 \\ {S}_1=\frac{c\cdot v}{2} \\ v=\frac{2\cdot S_1}{c}=\frac{2\cdot 30}{13}=\frac{60}{13}\doteq 4.6154\text{m} \\ c{c}_1=a^2 \\ c{c}_2=b^2 \\ {c}_1=\frac{a^2}{c}=\frac{5^2}{13}=\frac{25}{13}\doteq 1.9231\text{m} \\ {c}_2=\frac{b^2}{c}=\frac{12^2}{13}=\frac{144}{13}\doteq 11.0769\text{m} \\ S=\frac{c_2\cdot v}{2}=\frac{\frac{144}{13}\cdot \frac{60}{13}}{2}=\frac{4320}{169}{\text{m}}^2=25.5621{\text{m}}^2 \end{gathered}$$

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