 Hello friends, welcome to the session. I am Malkan. Today we are going to discuss the diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the field. So let's start with the solution now. Since we are not knowing the shorter side, the longer side and the diagonal, so first of all let us assume these three unknowns. Let the shorter side equal to x meters. Therefore the diagonal, which according to the question is 60 meters more than the shorter side, therefore diagonal equal to x plus 60 meters and the longer side will be x plus 30 meters. Now, now according to question our figure is, with the shorter side which is x, the longer side x plus 30 and the diagonal is x plus 60. We'll apply Pythagoras theorem in the right-angle triangle according to which hypotenuse square equal to side square plus base square. Now, we place the value and get in place of hypotenuse, we'll keep x plus 60 whole square equal to x square plus x plus 30 whole square. This implies x square plus 120 x plus 3600 equal to x square plus x square plus 60 x plus 900. This implies 2x square minus x square plus 60 x minus 120 x plus 900 minus 3600 equal to 0. This implies x square minus 60 x minus 2700 equal to 0. This is our quadratic equation. Now on comparing this equation with ax square plus vx plus c equal to 0, we get a equal to 1, v equal to minus 60 and c equal to minus 2700. Therefore, we can calculate the value of d which is b square minus 4ac. Now on substituting the value, we get minus 60 square minus 4 into 1 into minus 2700. This gives us d equal to 3600 plus 10,800. This implies d equal to 14,400. Now we'll calculate alpha and beta. We know alpha equal to minus b plus square root of d upon 2a and beta equal to minus b minus square root of d upon 2a. This gives alpha equal to minus of minus 60 plus square root of 14,400 upon 2 into 1. This implies alpha equal to plus 60 plus 120 upon 2. This implies alpha equal to 180 by 2. Therefore, alpha equal to 90. Now we'll calculate beta. We see that beta equal to minus b minus square root of d upon 2a. On substituting value, we get minus of minus 60 minus square root of 14,400 upon 2 into 1. We get plus 60 minus 120 upon 2. This implies beta equal to minus 60 upon 2. Therefore, beta equal to minus 30. Now length of the side cannot be negative. Therefore, we take alpha equal to 90 or x equal to 90, hence the shorter side which is x equal to 90. Longer side is x plus 30, which is equal to 90 plus 30 equal to 120. Hence the two sides are. Hope you understood the solution and enjoyed the session. Goodbye and take care.