ANSWER:
52 shrubs
STEP-BY-STEP EXPLANATION:
We know the number of trees planted in a given area, so to calculate the number of total trees, we must calculate the area of the entire figure and thus calculate by means of a proportion
We calculate the total area if we divide the figure in two, as follows:
The area of zone A, which is a rectangle, is calculated as follows:
![\begin{gathered} A_A=b\cdot h \\ A_A=50\cdot20 \\ A_A=1000 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A_A%3Db%5Ccdot%20h%20%5C%5C%20A_A%3D50%5Ccdot20%20%5C%5C%20A_A%3D1000%20%5Cend%7Bgathered%7D)
The area of zone B, which is a triangle, is calculated as follows:
![A_B=\frac{b\cdot h}{2}](https://tex.z-dn.net/?f=A_B%3D%5Cfrac%7Bb%5Ccdot%20h%7D%7B2%7D)
To calculate the value of the height of the triangle, we apply the Pythagorean theorem on the right triangle that is formed:
Where the hypotenuse is 25 meters and the other leg is 15 meters, just like this:
![\begin{gathered} h^2=a^2+b^2 \\ 25^2=15^2+b^2 \\ b=\sqrt[]{25^2-15^2} \\ b=\sqrt[]{400} \\ b=20 \\ \text{therefore the height is 20 meters, replacing:} \\ A_B=\frac{30\cdot20}{2} \\ A_B=300 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20h%5E2%3Da%5E2%2Bb%5E2%20%5C%5C%2025%5E2%3D15%5E2%2Bb%5E2%20%5C%5C%20b%3D%5Csqrt%5B%5D%7B25%5E2-15%5E2%7D%20%5C%5C%20b%3D%5Csqrt%5B%5D%7B400%7D%20%5C%5C%20b%3D20%20%5C%5C%20%5Ctext%7Btherefore%20the%20height%20is%2020%20meters%2C%20replacing%3A%7D%20%5C%5C%20A_B%3D%5Cfrac%7B30%5Ccdot20%7D%7B2%7D%20%5C%5C%20A_B%3D300%20%5Cend%7Bgathered%7D)
Now, the total area would be the sum of both areas:
![\begin{gathered} A_T=1000+300 \\ A_T=1300 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A_T%3D1000%2B300%20%5C%5C%20A_T%3D1300%20%5Cend%7Bgathered%7D)
Which means that if in an area of 400 square meters (20 * 20) they can plant 16 shrubs, in an area of 1300 square meters they would be:
![\begin{gathered} \frac{16}{400}=\frac{x}{1300} \\ \text{ solving for x} \\ x=\frac{16\cdot1300}{400} \\ x=52 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B16%7D%7B400%7D%3D%5Cfrac%7Bx%7D%7B1300%7D%20%5C%5C%20%5Ctext%7B%20solving%20for%20x%7D%20%5C%5C%20x%3D%5Cfrac%7B16%5Ccdot1300%7D%7B400%7D%20%5C%5C%20x%3D52%20%5Cend%7Bgathered%7D)
In other words, a total of 52 shrubs can be raised throughout the region.