The height of a trapezium is 68 cm, and the sum of its parallel sides is 75 cm. If the area of the trapezium is $$\frac{6}{17}$$, times of the area of a square, then the length of the diagonal of the square is: (in cm) (Take ,$$\sqrt{2} = 1.4 1$$)

The height of a trapezium is 68 cm, and the sum of its parallel sides is 75 cm.

Area of a trapezium = $$\frac{1}{2}\times sum\ of\ its\ parallel\ sides\ \times height\ $$

= $$\frac{1}{2}\times75\ \times68\ $$

If the area of the trapezium is $$\frac{6}{17}$$, times of the area of a square.

area of the trapezium = $$\frac{6}{17}$$ of the area of a square

$$425 = \frac{1}{17}\times(length\ of\ side\ of\ square)^2$$

$$(length\ of\ side\ of\ square)^2 = 7225$$

$$(length\ of\ side\ of\ square)^2 = 85^2$$

length of side of square = 85 cm

Length of the diagonal of the square = $$\sqrt{2}\times(length\ of\ side\ of\ square)$$

= $$1.41\times85$$

= 119.85 cm