Represent the following situations with suitable mathematical equations.
The hypotenuse of a right triangle is 25 cm. We know that the difference in lengths of the other two sides is 5 cm. We would like to find out the length of the two sides?

The hypotenuse of a right angled triangle is 25cm an dits perimeter 56 cm. Find the length of the smallest side.

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Represent the following situations with suitable mathematical equations. Sridhar and Rajendar together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles now they have is 124. We would like to find out how many marbles each of them had previously.

Represent the following situations in the form of quadratic equation: The product of two consecutive positive integers is 306. We need to find the integers.

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

If two side of a triangle are hat i+2 hat ja n d hat i+ hat k , then find the length of the third side.

Altitude on the hypotenuse of a right angle triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude.

Construct a right triangle whose base is 7.5cm. and sum of its hypotenuse and other side is 15cm.

Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.