In right ` triangle A B C ,` the lengths of the legs are given. Find the length of the hypotenuse.
(i) `a=6\ c m ,\ b=8\ c m\ `
(ii) `a=8\ c m ,\ b=15\ c m`
(iii) `a=3\ c m ,\ b=4\ c m`
(iv) `a=2\ c m ,\ b=1. 5\ c m`

The sides of certain triangles are given below. Determine which of them are right triangles. (i) a=7c m , b=24 c m and c=25 c m (ii) a=9c m , b=16 c m and c=18 c m (iii) a=1. 6 c m , b=3. 8 c m and c=4c m (iv) a=8c m , b=10 c m and c=6c m

The sides of certain triangles are given below. Determine which of them are right triangles: (i) a=6c m , b=8c m and c=10 c m (ii) a=5c m , b=8c m and c=11 c m .

Construct a triangle A B C if the lengths of its sides are given by A B=6\ c m ,\ B C=7\ c m and A C=5\ c mdot

Find the area of the pentagon shown in Figure, if A D=10 c m ,\ A G=8c m ,\ A H=6c m ,\ A F=5c m ,\ B F=5c m ,\ C G=7c m\ a n d\ E H=3c mdot

Construct a right triangle A B C whose base B C is 6\ c m and the sum of hypotenuse A C\ and other side A B is 10\ c m

Find the area, in square metres, of a rectangle whose (i) Length = 4. 5\ m , breadth = 1. 6\ m (ii) Length = 720\ c m , breadth = 25\ c m (iii) Length = 3\ d m\ 6\ c m , breadth = 2\ d m\ 9\ c mdot

Which of the following pairs of triangles are congruent? If they are congruent, write out the pairs of equal angles. A B C : A B=3c m ,\ B C=4c m ,\ C A=2\ c m D E F : D E=2\ c m ,\ E F=3\ c m\ a n d\ F D=4\ c m P Q R : P Q=17\ c m ,\ Q R=15\ c m ,\ P R=18\ c m D E F : D E=18\ c m ,\ E F=17\ c m ,\ D F=15\ c m .

Find the area of the quadrilateral A B C D , in which A B=7c m ,B C=6c m ,C D=12 c m ,D A=15 cm and A C=9 cm

In which of the following cases can a right triangle A B C be constructed? (a) A B=5\ c m ,\ B C=7\ c m ,\ A C=10\ c m (b) A B=7\ c m ,\ B C=8\ c m ,\ A C=12\ c m (c) A B=8\ c m ,\ B C=17\ c m ,\ A C=15\ c m (d) None of these

In a right triangle A B C right angled at B , /_A C B=theta , A B=2c m and B C=1\ c m . Find the value of sin^2theta+tan^2theta .