Answer:
The length of the longer base is 80 feet.
Step-by-step explanation:
We are given that county courthouse is shaped like a trapezoid.
Let the height of the court house be h
Since we are given that The shorter base of the trapezoid is 15 feet longer than the height.
So, the shorter base = h+15
We are also given that The longer base is 5 feet longer than 3 times the height
So, longer Base = 3h+5
Now we are also given that the area of the landing is 1500 square feet.
Formula of area of trapezium :
=![\frac{1}{2} *(\text{Length of longer base}+\text{Length of shorter base})*height](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%2A%28%5Ctext%7BLength%20of%20longer%20base%7D%2B%5Ctext%7BLength%20of%20shorter%20base%7D%29%2Aheight)
Substituting the values .
![1500=\frac{1}{2} *(h+15+3h+5)*h](https://tex.z-dn.net/?f=1500%3D%5Cfrac%7B1%7D%7B2%7D%20%2A%28h%2B15%2B3h%2B5%29%2Ah)
![1500=\frac{1}{2} *(4h+20)*h](https://tex.z-dn.net/?f=1500%3D%5Cfrac%7B1%7D%7B2%7D%20%2A%284h%2B20%29%2Ah)
![1500*2=(4h+20)*h](https://tex.z-dn.net/?f=1500%2A2%3D%284h%2B20%29%2Ah)
![3000=4h^2+20h](https://tex.z-dn.net/?f=3000%3D4h%5E2%2B20h)
Taking 4 common from the equation.
![750=h^2+5h](https://tex.z-dn.net/?f=750%3Dh%5E2%2B5h)
![h^2+5h-750=0](https://tex.z-dn.net/?f=h%5E2%2B5h-750%3D0)
![h^2-25h+30h-750=0](https://tex.z-dn.net/?f=h%5E2-25h%2B30h-750%3D0)
![h(h-25)+30(h-25)=0](https://tex.z-dn.net/?f=h%28h-25%29%2B30%28h-25%29%3D0)
![(h-25)(h+30)=0](https://tex.z-dn.net/?f=%28h-25%29%28h%2B30%29%3D0)
⇒ h = 25, -30
Neglect the negative value .
So, height = 25 feet.
Length of Longer base = 3h+5 =3*25+5=80 feet
Hence , the length of the longer base is 80 feet.