Question

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?

Answer 1

The length of the longer base is 80 feet.

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 :

=
`(1)/(2) *(\text{Length of longer base}+\text{Length of shorter base})*height`

Substituting the values .

`1500=(1)/(2) *(h+15+3h+5)*h`

`1500=(1)/(2) *(4h+20)*h`

`1500*2=(4h+20)*h`

`3000=4h^2+20h`

Taking 4 common from the equation.

`750=h^2+5h`

`h^2+5h-750=0`

`h^2-25h+30h-750=0`

`h(h-25)+30(h-25)=0`

`(h-25)(h+30)=0`

⇒ 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.