A rhombus sheet whose perimeter is 40 m and one diagonal is 12 m long painted on both sides @ Rs 5 per square m.Find the cost of the painting ?

Asked by Vikas | 18th May, 2017, 11:02: PM

Expert Answer:

begin mathsize 14px style Perimeter equals 40 space straight m
rightwards double arrow 4 straight a equals 40 space straight m
rightwards double arrow straight a equals 10 space straight m

Let space diagonal space AC equals 12 space straight m
rightwards double arrow OA equals 6 space straight m
therefore space OB squared equals AB squared minus OA squared
rightwards double arrow OB equals square root of 10 squared minus 6 squared end root equals square root of 100 minus 36 end root equals square root of 64 equals 8 space straight m
rightwards double arrow BD equals 2 OB equals 2 cross times 8 equals 16 space straight m
Area space of space sheet equals 1 half cross times AC cross times BD equals 1 half cross times 12 cross times 16 equals 96 space straight m squared
Cost space of space painting space on space both space sides space at space the space rate space of space Rs. space 5 space per space straight m squared
equals Rs. space left parenthesis 5 cross times 2 cross times 96 right parenthesis
equals Rs. space 960 end style

Answered by Rashmi Khot | 19th May, 2017, 09:10: AM