The lengths of parallel sides of a trapezium are (x + 9) cm and (2x - 3) cm , and the distance between them is (x + 4) cm . If its area is 540 cm² , find x .

If the sum of two smaller sides of a right-angled triangle is 17 cm and the perimeter is 30 cm, then find the area of the triangle.

The perimeter of a rectangular plot is 180 m and its area is 1800 m². Take the length of the plot as x meters. Use the perimeter 180 m to write the value of the breadth in terms of x . Use the values of length, breadth and the area to write an equation in x . Solve the equation to calculate the length and breadth of the plot.

The hypotenuse of a grassy land in the shape of a right triangle is 1 metre more than twice the shortest side. If the third side is 7 metres more than the shortest side, find the sides of the grassy land.