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ICSE Class 8 Answered

The length and breadth of a rectangular park are in ratio of 5:2.a 2.5 m wide path running all around the outside of the park has an area of 305 m2 find the dimensions of the park  
Asked by Asindhu75 | 23 Jul, 2018, 08:29: AM
answered-by-expert Expert Answer
begin mathsize 16px style Let space the space length space of space the space park space equals space 5 straight a space
breadth space equals space 2 straight a space
Therefore comma space
Area space of space the space rectangular space park space equals space 5 straight a space cross times space 2 straight a space equals space 10 straight a squared
Width space of space the space path space equals space 2.5 space straight a
Outer space length space PQ space equals space 5 straight a space plus 2.5 space plus space 2.5 space equals space 5 straight a space plus 5
Outer space length space QR space equals space 2 straight a space plus 2.5 space plus space 2.5 space equals space 2 straight a space plus 5
Area space of space PQRS space equals space left parenthesis 5 straight a space plus 5 right parenthesis space left parenthesis 2 straight a space plus 5 right parenthesis equals space 10 straight a squared space plus space 35 space straight a space plus space 25
Area space of space the space path space equals space open square brackets open parentheses 10 straight a squared space plus space 35 space straight a space plus space 25 close parentheses space minus space 10 straight a squared close square brackets
rightwards double arrow space 305 space equals space 35 straight a space plus space 25
rightwards double arrow straight a space equals space 280 over 35 space equals space 8
Therefore comma
length space of space the space park space equals space 5 straight a space equals space 5 space cross times space 8 space equals space 40 space straight m
breadth space of space the space park space equals space 2 straight a space equals space 2 space cross times space 8 space equals space 16 space straight m

end style
Answered by Yasmeen Khan | 23 Jul, 2018, 11:04: AM
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