 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that the floor of our room is 16 feet by 11 feet and its height is 9 feet. Find the distance from a corner point on the floor to the opposite corner on the ceiling. We know that Pythagoras theorem states that in our right-angle triangle with hypotenuse c, like a and b, we have c squared is equal to a squared plus b squared. That is, square of length of hypotenuse is equal to sum of squares of length of the legs. With this key idea, let us proceed to the solution. In this question, we are given a room whose dimensions are 16 feet by 11 feet and height is 9 feet. Shape of room is in a cuboid form whose all corners are at 90 degrees. In this diagram, we have drawn a cuboid with length bd that is 16 feet and width cd that is 11 feet. Height of cuboid ac is given by 9 feet. We have to find the distance from a corner point on the floor to the opposite corner on the ceiling. So, let a be the point on the corner of ceiling and b be the point on the opposite corner on the floor. We join a b and this is the distance we need to find. So, we have point a as the point on the corner of the ceiling and point b is the point on the opposite corner of the floor. Now, let c be the point on the corner of floor such that triangle a b c is a right angle triangle a b c is a right angle triangle where angle c is 90 degrees. Then, we have ac as the height of the room which is equal to 9 feet and let b c be equal to x feet and a b be equal to y feet. Now, in the figure we see that d is one corner of the floor. We also see that points b c and d form a right angle triangle that is triangle b c d is a right angle triangle. In triangle b c d we know that b d is the length of the room and is given as 16 feet, c d is the width of the room and is given as 11 feet and b c is equal to x feet. And according to the question we need to find the value of y that is the distance a b to find the value of y we need to find the value x first so that we can apply Ithagoras theorem in triangle a b c. From the key idea we know that Ithagoras theorem states that in a right angle triangle with hypotenuse c and legs a and b we have c square is equal to a square plus b square. So, applying Ithagoras theorem in the right angle triangle b c d we say that b c square is equal to b d square plus c d square. Since we know that triangle b c d is a right angle triangle with angle d as 90 degrees so hypotenuse b c square will be equal to the sum of the squares of the legs c d and b d. So, we say that b c square that is x square is equal to b d square that is 16 square plus c d square which is equal to 11 square. That is x square is equal to 16 square that is 256 plus 11 square that is 121 so we get 256 plus 121 that is 377. So, we say that x square is equal to 377. Now in triangle a b c I'm applying Ithagoras theorem we say that the hypotenuse a b square will be equal to sum of the squares of the legs of the triangle. That is a c square plus b c square and we know that a b is equal to y so a b square would be y square is equal to a c square that is 9 square plus b c square which is equal to x square. So, we get y square is equal to 9 square that is 81 plus x square and we know that x square is equal to 377. So, we write 377 and therefore we get y square as 458 that is we add 81 and 377 which implies that y is equal to square root of 458. Now taking the square root of y we get the value of y as 21.4 approximately that we can say that the distance a b is given by 21.4 feet approximately which is the required answer. This completes our session. Hope you enjoyed this session.