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 :
=[tex]\frac{1}{2} *(\text{Length of longer base}+\text{Length of shorter base})*height[/tex]
Substituting the values .
[tex]1500=\frac{1}{2} *(h+15+3h+5)*h[/tex]
[tex]1500=\frac{1}{2} *(4h+20)*h[/tex]
[tex]1500*2=(4h+20)*h[/tex]
[tex]3000=4h^2+20h[/tex]
Taking 4 common from the equation.
[tex]750=h^2+5h[/tex]
[tex]h^2+5h-750=0[/tex]
[tex]h^2-25h+30h-750=0[/tex]
[tex]h(h-25)+30(h-25)=0[/tex]
[tex](h-25)(h+30)=0[/tex]
⇒ 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.
