If the sum of the lengths of the hypotenuse and a side of a right-angled triangle is given, show that the area of triangle is maximum when the angle between them is 60^(@) .

Draw a right triangle in which ( other than the hypoten use ) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.

The hypotenuse of a right triangle is 6m more than twice of the shortest side. If the third side is 2 m., less than the hypotenuse, find the sides of the triangle

Draw a right-angled triangle where the sides other than the hypotenuse are of lengths 2.2 cm and 2.2 cm. Then, construct another triangle whose sides are (5)/(3) times the corresponding sides of the given triangle.

Construct a right-triangle where the sides (other than the hypotenuse) are of lengths 5 cm and 7 cm. Then, construct another triangle whose sides are (4)/(5) times the corresponding sides of the given triangle.

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are (5)/(2) times the corresponding sides of the given triangle.

The perimeter of angled triangle is 30 cm and its hypotenuse is 13 cm. Find the length of other two sides of triangle.

In each of the following, give the justification of the construction too. Draw a right-triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then, construct another triangle whose sides are (5)/(3) times the corresponding sides of the given triangle.

Construct a triangle with sides 5 cm, 5.5 cm, and 6.5 cm. Construct another triangle whose sides are (3)/(5) times the corresponding sides of the given triangle.