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`

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

Triangle A B C is right angled at AdotA D is perpendicular to B Cdot If A B=5 c m , B C=13 c m and A C=12 c mdot Find the area of A B Cdot Also, find the length of A Ddot

If a, b,c are the lengths of the sides of triangle , then

In Fig. 10.97, the sides A B ,\ B C and C A of triangle A B C , touch a circle at P ,\ Q and R respectively. If P A=4c m , B P=3c m and A C=11 c m , then length of B C is (FIGURE) (a) 11cm (b) 10cm (c) 14cm (d) 15cm

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 triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ C A\ a n d\ A B respectively. If A C=21\ c m ,\ B C=29 c m\ a n d\ A B=30 c m , find the perimeter of the quadrilateral A R P Q

In Fig. 10.103, a quadrilateral A B C D is drawn to circumscribe a circle such that its sides A B ,\ B C ,\ C D and A D touch the circle at P ,\ Q ,\ R and S respectively. If A B=x\ c m , B C=7c m , C R=3c m and A S=5c m , then x= (FIGURE) (a) 10 (b) 9 (c) 8 (d) 7

Draw a triangle A B C with A B=6\ c m ,\ B C=7\ c m and C A=8\ c mdot Using ruler and compass alone, draw (i) the bisector A D\ of \ /_A and (ii) perpendicular A L from A on B Cdot Measure L A Ddot

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

A B C is a triangle and P Q is a straight line meeting A B in P and A C in Q . If A P=1c m , P B=3c m , A Q=1. 5 c m , Q C=4. 5 m , prove that area of A P Q is one-sixteenth of the area of A B C .