The dimensions of a rectangle ABCD are `"51 cm" xx "15 cm". A trapezium PQCD with its parallel sides QC and PD in the ratio 9:8, is cut off from the rectangle as shown in the figure. If the area of the trapezium PQCD is `(5)/(6)` th part of the area of the rectangle. Find the length QC and PD.

Explanation

`"We have dimensions of a recstangle ABCD as 51 cm and 25 cm. Also, in trapezium PQCD, parallel sides QC and PD are in the ratio 9:8"`.
`i.e.," "QC:PD=9:8`
`"Let,length" " " QC=9x`
`"and" " " PD=8x`

`"According to the question"`,
`"Area of trapezium" PQCD=(5)/(6) " area of rectangle ABCD"`
`rArr (1)/(2)("Sum of parallel sides")xx"Distance betwen parallel sides"=(5)/(6)xx(BCxxCD)`
`rArr " " (1)/(2)(8x+9x)xx25=(5)/(6)xx51xx25`
`rArr " " (1)/(2)xx"17x"xx25=(5)/(6)xx51xx25`
`rArr " " x=(5xx51xx25xx2)/(25xx17xx6)`
`rArr " " x=5`
`therefore"Lengths," " "QC=9xx5=45cm`
`"and" " "PD=8xx5=40cm`