The landing for the steps leading up to a county courthouse is shaped like a trapezoid. the area of the landing is 1500 square feet. the shorter base of the trapezoid is 15 feet longer than the height. the longer base is 5 feet longer than 3 times the height. what is the length of the longer base?

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.

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