Question

one base of a trapezoid is 3 times the length of the second base. the height of the trapezoid is 2in smaller than the second base if the area is 30 what is the length of both bases

Answer 1

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

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 =
`3x`

Also Given:

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

So we can say that;

Height of the trapezoid =
`x-2`

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;

`(x+3x)/(2)*(x-2)=30\\\\(4x)/(2)* (x-2)=30\\\\2x(x-2)=30`

Now Dividing both side by 2 we get;

`(2x)/(2)(x-2)=(30)/(2)\\\\x(x-2)=15\\\\x^2-2x-15=0`

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

`x^2-5x+3x-15=0\\\\x(x-5)+3(x-5)=0\\\\(x+3)(x-5)=0`

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

`x+3=0 \ \ \ \ Or \ \ \ \ \ \ x-5=0\\\\x=-3 \ \ \ \ \ \ \ Or \ \ \ \ \ \ x=5`

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 =
`3x=3*5 =15\ in`

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