The dimensions of a rectangle ABCD are 51 cm x 25 cm. A trapezium PQCD

1.	The dimensions of a rectangle ABCD are 51 cm x 25 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 lengths QC and PD.
Answer» Area of rectangle (ABCD) = BC × CD ⇒ Area of rectangle (ABCD) = 51 × 25 = 1275 cm² Area of trapezium PQCD = 5/6 × Area of rectangle (ABCD) ⇒ Area of trapezium PQCD = 5/6 × 1275 = 1062.5 cm² Given that QC:PD = 9:8 Let QC = 9x and PD = 8x Area (PQCD) = (Sum of parallel sides)/2 x Height ⇒ Area (PQCD) = (9x + 8x)/2 x 25 ⇒ 1062.5 = (17x)/2 x 25 ⇒ 85 = 17x ⇒ x = 5cm QC = 9x = 45cm PD = 8x = 40 cm

The dimensions of a rectangle ABCD are 51 cm x 25 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 lengths QC and PD.

Answer»

Area of rectangle (ABCD) = BC × CD

⇒ Area of rectangle (ABCD) = 51 × 25 = 1275 cm²

Area of trapezium PQCD = 5/6 × Area of rectangle (ABCD)

⇒ Area of trapezium PQCD = 5/6 × 1275 = 1062.5 cm²

Given that QC:PD = 9:8

Let QC = 9x and PD = 8x

Area (PQCD) = (Sum of parallel sides)/2 x Height

⇒ Area (PQCD) = (9x + 8x)/2 x 25

⇒ 1062.5 = (17x)/2 x 25

⇒ 85 = 17x

⇒ x = 5cm

QC = 9x = 45cm

PD = 8x = 40 cm