In the figure i given below PB and QA are perpendiculars to the line segment AB If PO 6 cm QO 9 cm a...

Question

In the figure i given below PB and QA are perpendiculars to the line segment AB If PO 6 cm QO 9 cm and the area of POB 120 cm find the area of QOA

Accepted Answer

Solution The square of any ratio between any two corresponding sides of two similar triangles is equal to the ratio of their areas From the question it is given that PO 6 cm QO 9 cm and the area of POB 120 cm From the figure Consider the AOQ and BOP OAQ OBP both angles are equal to 90suposup AOQ BOP because vertically opposite angles are equal Therefore AOQ BOP Then area of AOQarea of BOP OQsup2supPOsup2sup Area of AOQ120 9sup2sup6sup2sup Area of AOQ120 8136 Area of AOQ 81 12036 Area of AOQ 270 cmsup2sup

ML Aggarwal Solutions Class 10 Mathematics Solutions for Similarity Exercise 13.3 in Chapter 13 - Similarity