 Hello and welcome to the session. In this session we discussed the following question which says, find the length of the altitude Pt of an isosceles triangle PQR in which PQ is equal to PR is equal to 2x units and QR is equal to x units. Before we move on to the solution let's recall the RHS criteria for congruence of right triangles. According to this we have that two right angles triangles are congruent if one side and the hypotenuse of one are respectively equal to the corresponding side of the hypotenuse of the other. This is the key idea that we use for this question. Now let's see the solution. So here we are given the isosceles triangle PQR in which we have PQ is equal to PR is equal to 2x units then QR is equal to x units and this Pt is the altitude of triangle PQR. We need to find the length of this Pt. Consider the right triangles PQT and PRT in this we have PQ is equal to PR which is given to us and PQ and PR are respectively the hypotenuse of triangles PQT and PRT and side Pt is equal to Pt since it is the common side for both the triangles. So therefore triangle PQT is congruent to the triangle PRT by the RHS criteria. Now since both these triangles are congruent so this means that PQT is equal to PR since they are the corresponding parts of the congruent triangles and this means that Pt is the point of the side QR of triangle PQR. Now as we are given that QR is equal to x units and Qt is equal to PR, Qt equal to PR would be equal to x upon 2 units. Now if you consider the right triangle PQT in this by the Pythagoras theorem we have PQ square is equal to Pt square plus TQ square we are already given that PQ is equal to 2x then Qt is equal to x upon 2 so we have that 2x whole square is equal to Pt square plus x upon 2 whole square which means we have third x square is equal to Pt square plus x square upon 4 from where we get Pt square is equal to 4x square minus x square upon 4 this gives us Pt square equal to 16x square minus x square upon 4 of Pt square is equal to 15x square upon 4 so from here we get Pt is equal to x into root 15 upon 2 units. We were supposed to find the length of this altitude Pt and this comes out to be equal to root 15x upon 2 units. So this completes our session, hope you have understood the solution of this question.