 Hello and welcome to the session. In this session we are going to discuss how to use Pythagorean theorem to solve problems with right triangles, rectangles and combined problems. We know that Pythagorean theorem states sum of squares of the length of sites of a right-angle triangle is equal to the square of the length of the hypotenuse. Or this can also be stated as in our right-angled triangle with hypotenuse c and sites a and b we have c square is equal to a square plus b square. Now we shall apply this theorem to the following problems based on rectangles. Suppose Jain has a television set of size 20 inches, size measured diagonally. If width of the screen is 16 inches, then what is the length of the television screen? Let us start with the solution of this problem. Here we are given size of television is 20 inches. It means the measure of the screen diagonally is 20 inches, its width is 16 inches and we have to find its length. Shape of the television is of a rectangle. Now let the length of this rectangular television set be x inches and we know that all the angles in a rectangle are of 90 degrees. So this angle will be 90 degrees. Let us denote the width of this rectangular television set by a which is given as 16 inches and length of this diagonal be denoted by c which is given as 20 inches. Now these two sides and this diagonal form a right-angled triangle where diagonal forms the hypotenuse. So we can apply Pythagoras theorem here. Hypotenuse c is equal to 20, side a is equal to 16 and side b is equal to x. Using Pythagoras theorem we know that a square plus b square will be equal to c square that is 16 square plus x square will be equal to 20 square. Which implies that x square will be equal to 20 square minus 16 square that is x square will be equal to 400 minus 256. Which implies x square is equal to 144 that is x is equal to square root of 144. This implies x is equal to now taking positive square root because length is never negative. Here we get x is equal to 12. So length of TV set will be equal to 12 inches. Let us consider one more problem. From this figure find the area of the square a, b, c, d. Now if we look at this given figure here vertices a, b, c, d form a square and vertices o, c, d form a right-angled triangle which is right-angled at o. Also measure of side o, c of the triangle is given as 13 centimeters and measure of side o, d is given as 5 centimeters and we have to find the area of the square a, b, c, d. We know that area of square is given by side square. So if we find one side of the square we can find its area. From this figure c, side c, d of the square is also the hypotenuse of the right-angled triangle o, c, d. So in right-angled triangle o, c, d, o, c is equal to 13 centimeters and o, d is equal to 5 centimeters and we have to find the length of side c, d. So applying Pythagoras theorem here we get o, c square plus o, d square is equal to c, d square. Now we substitute the value of o, c and o, d here and we get 13 square plus 5 square is equal to c, d square. Or we can also write it as c, d square is equal to 13 square plus 5 square which implies that c, d square will be equal to 169 plus 25 which further implies that c, d square is equal to 194. Now here we can see that c, d is one side of the square a, b, c, d and area of the square is equal to side square. So using these two results we can say that area of square which is equal to side square that is equal to c, d square is 194 square centimeters. Thus using Pythagorean theorem we can solve problems with right triangles, rectangles and combined problems. This completes our session. Hope you enjoyed this session.