The area of a trapezium is `180 cm^2` and its height is `9 cm`. If one of the parallel sides is longer than the other by 6 cm, the length of the longer of the parallel sides is

Explanation

Given
area of trapezium `=180cm^2` and
height=9cm.
If one of the parallel sides is longer than the other by `6 cm` then
we need the find the two parallel sides of trpizium.
Let the length of the shorter parallel side be `x cm`.
then the length of the longer side is `= (x+6)cm`.
we know that area of trapezium `=(1/2)xx`(sum of parallel sides)`xx`height.
Using known values,we get
`180=[(x+x+6)/2]xx9`
`implies 2x+6=40`
`implies x=17`.
therefore ,length of parallel sides are `17cm` and `17+6=23cm`.
Hence longer sides of parallel sides is `23cm`