Question

6. The area of a trapezium is 385 cm². Its parallel sides are in the ratio 3:4 and the perpendicular distance between them is 11 cm. Its longer side is : (a) 35 cm (b) 30 cm (c) 40 cm (d) 60 cm​

Answer 1

Answer:

The longer side is 40cm.

Step-by-step explanation:

It has been mentioned here that the area of the respective trapezium is

385$cm^{2}$  The parallel sides of the same trapezium are in the ratio of 3:4 and the perpendicular distance between the two is given to be 11 cm. We have to calculate its longer side as below:

Let the two sides of the trapezium be 3m and 4m respectively.

Now we have the area of the trapezium as below:

Area = $\frac{1}{2}$ × (sum of parallel sides) × height

∴ 385 = $\frac{1}{2}$ ( 3m + 4m) × 11

⇒ 385 × 2 = 7m × 11

⇒ 770 = 77m

⇒ 77m = 770

⇒ m = 770 ÷ 77

⇒ m = 10

Therefore the parallel sides are:

3m = 3 × 10 cm = 30cm

4m = 4 × 10 cm = 40 cm

Therefore the longer side is equal to 40 cm.