**Answer:**

**Length of bases of the trapezoid are 5 inch and 15 inch.**

**Step-by-step explanation:**

Let the length of the second base be 'x'.

Given:

one base of a trapezoid is 3 times the length of the second base.

So we can say that;

Length of the first base =

Also Given:

the height of the trapezoid is 2 in smaller than the second base

So we can say that;

Height of the trapezoid =

Area of the trapezoid = 30

We need to find the length of both the bases.

Solution:

Now we know that;

**Area of trapezoid is equal to half of the sum of the length of two bases multiplied by height of the trapezoid.**

framing in equation form we get;

**Now Dividing both side by 2 we get;**

**Now we will find the roots by factorizing the equation we get;**

**Now we find the values of x by solving separately we get;**

**Now we have got 2 values of 'x' one positive and one negative.**

**Now we know that length of the base of trapezoid cannot be negative hence we will discard it and consider the positive value of 'x'.**

Length of second base = 5 in

Length of first base =

**Hence Length of base of the trapezoid are 5 inch and 15 inch.**