 Hi and welcome to the session. Let us discuss the following question. The question says, the sides of a right-angled triangle containing the right angle are 3 x plus 1 cm and 2 x minus 1 cm. If the area of the triangle is 30 square cm, calculate the length of the sides of the triangle. This is the right triangle ABC and these are the two sides containing the right angle. We have to find the length of the sides of the triangle. Let us now begin with the solution. We know that area of triangle ABC is given by half base into height. Now here we are given that area of triangle is 30 square cm. This is 2 x minus 1 and height is 3 into x plus 1. This implies 60 is equal to 2 x minus 1 into 3 x plus 3. This implies 60 is equal to 6 x square plus 6 x minus 3 x minus 3. This implies 60 is equal to 6 x square plus 3 x minus 3. This implies 6 x square plus 3 x minus 3 minus 60 is equal to 0. This implies 6 x square plus 3 x minus 63 is equal to 0. This implies 2 x square plus x minus 21 is equal to 0. This implies 2 x square plus 7 x minus 6 x minus 21 is equal to 0. We have split at the middle top. This implies x into 2 x plus 7 minus 3 into 2 x plus 7 is equal to 0. This implies x minus 3 into 2 x plus 7 is equal to 0. This implies x minus 3 is equal to 0 or 2 x plus 7 is equal to 0. This implies x is equal to 3 or x is equal to minus 7 by 2. We know that length of the triangle cannot be negative. So x equals to minus 7 by 2 is not possible. This implies x is equal to 3. So a b is equal to 3 into x plus 1. That is 3 into 3 plus 1. That is 12 centimeters. b c is equal to 2 x minus 1. That is 2 into 3 minus 1. That is 5 centimeters. But Pythagoras theorem in right triangle a b c a c square is equal to a b square plus b c square. Now a b is equal to 12 centimeters. So this is equal to 12 square plus 5 square. This is equal to 144 plus 25 and this is equal to 169. So a c square is equal to 169 and this implies a c is equal to 13 centimeters. So length of the sides of a triangle are 13 centimeters, 12 centimeters and 5 centimeters. This is our required answer. So this concludes the session. Bye and take care.