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`

Find the area of the triangle in which Q(i) a = 13 m, b=14 m, c=15 m, (ii) a = 52 cm, b = 56 cm, c = 60 cm, (iii) a = 91 m, b=98 m. c = 105 m.

The sides of certain triangles are given below. Determine which of them are right triangles. 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

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

In a A B C , D a n d E are points on the sides A B and A C respectively. For each of the following cases show that D E B C : A B=12 c m , A D=8 c m , A E=12 c m a n d A C=18 c m . (ii) A B=5. 6 c m , A D=1. 4 c m , A C=7. 2 c m a n d A E=1. 8 cm

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

In a A B C ,\ \ D\ a n d\ E are points on the sides A B and A C respectively. For each of the following cases show that D E B C : A B=10. 8 c m ,\ \ B D=4. 5\ c m ,\ \ A C=4. 8 c m\ a n d\ A E=2. 8 c m (ii) A D=5. 7 c m ,\ \ B D=9. 5 c m ,\ \ A E=3. 3 c m\ a n d\ E C=5. 5 c m .

The area of a right isosceles triangle whose hypotenuse is 16sqrt(2)\ c m is 125 c m^2 (b) 158 c m^2 128 c m^2 (d) 144 c m^2

In Figure, if A C is bisector fo /_B A D such that A B=3\ c m\ a n d\ A C=5\ c m , then C D= 2\ c m (b) 3\ c m (c) 4\ c m (d) 5\ c m

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 .

In Fig. 4.60, check whether A D is the bisector of /_A of A B C in each of the following: (FIGURE) A B=5c m , A C=10 c m , B D=1. 5 c m and C D=3. 5 c m (ii) A B=4c m , A C=6c m , B D=1. 6 c m and C D=2. 4 c m (iii) A B=8c m , A C=24 c m , B D=6c m and B C=24 c m