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Bess [88]
3 years ago
9

The landing for the steps leading up to a county courthouse is shaped like a trapezoid. The area of the landing is 1500 square f

eet. 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?
Mathematics
1 answer:
77julia77 [94]3 years ago
6 0

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

Substituting the values .

1500=\frac{1}{2} *(h+15+3h+5)*h

1500=\frac{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.

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