iF PERIMETER OF A RECTANGLE AND A SQUARE IS 60 AND THE AREA OF THE SQUARE EXCEEDS AREA OF RECTANGLE BY 16 THEN FIND LENGTH OF THE RECTANGLE.

Asked by rameshgoc | 27th Aug, 2015, 08:43: AM

Expert Answer:

begin mathsize 14px style Perimeter space of space rectangle equals 2 left parenthesis straight l plus straight b right parenthesis equals 60 rightwards double arrow straight l plus straight b equals 30 rightwards double arrow straight b equals 30 minus straight l Perimeter space of space square equals 4 left parenthesis side right parenthesis equals 60 rightwards double arrow side equals 15 Now comma space Area left parenthesis square right parenthesis minus Area left parenthesis rectangle right parenthesis equals 16 rightwards double arrow left parenthesis side right parenthesis squared minus left parenthesis straight l cross times straight b right parenthesis equals 16 rightwards double arrow left parenthesis 15 right parenthesis squared minus straight l left parenthesis 30 minus straight l right parenthesis equals 16 rightwards double arrow 225 minus 30 straight l plus straight l squared equals 16 rightwards double arrow straight l squared minus 30 straight l plus 209 equals 0 rightwards double arrow straight l squared minus 19 straight l minus 11 straight l plus 209 equals 0 rightwards double arrow straight l left parenthesis straight l minus 19 right parenthesis minus 11 left parenthesis straight l minus 19 right parenthesis equals 0 rightwards double arrow left parenthesis straight l minus 19 right parenthesis left parenthesis straight l minus 11 right parenthesis equals 0 rightwards double arrow straight l equals 19 space or space straight l equals 11 Since comma space length space has space to space be space greater space tha space breadth comma space we space have space length space equals space 19 end style

Answered by Rashmi Khot | 27th Aug, 2015, 10:09: AM