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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 :
=
Substituting the values .
Taking 4 common from the equation.
⇒ 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.