Area of RT

In the right triangle has orthogonal projections of legs to the hypotenuse lengths 15 cm and 9 cm. Determine the area of ​​this triangle.

Correct answer:

S =  139.4 cm²

Step-by-step explanation:

$$\begin{gathered} p=15\text{ cm } \\ q=9\text{ cm } \\ c=p+q=15+9=24\text{ cm } \\ h=\sqrt{p\cdot q}=\sqrt{15\cdot 9}=3\sqrt{15}\text{ cm}\doteq 11.619\text{ cm } \\ S={\displaystyle \frac{c\cdot h}{2}}={\displaystyle \frac{24\cdot 11.619}{2}}=36\sqrt{15}=139.4{\text{cm}}^2 \end{gathered}$$

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