The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

The hypotenuse of a right triangle is 1 m less than twice the shortest side. If the third side is 1 m more than the shortest side, find the sides of the triangle.

The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

The length of a rectangle is twice as long as the side of a square. The side of the square is 4 cm more than the width of the rectangle. If their areas are equal, find their dimensions.

Prove that the difference of any two sides of a triangle is less than the third side.

Prove that the difference of any two sides of a triangle is less than the third side.

Sum of any two sides of a triangle is greater than the third side.

Represent the following situations in the form of quadratic equations. The area of a rectangular plot is 528m^(2) . The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

The perimeter of a triangular field is 144 cm and the ratio of the sides is 3:4:5. Find the area of the field.

State whether true or false Sum of any two sides of the triangle is less than the third side.