A rectangular carpet has an area of 120 sq metres and a perimeter of 46 metres. The length of
its diagonal (in metres) is:
1
Expert's answer
2013-03-29T12:05:54-0400
A rectangular carpet has an area of 120 sq metres and a perimeterof 46 metres. The length of its diagonal (in metres) is:
Suppose, rectangular has lengtha and width b. Then, an areaof rectangular equals: (1) S = a*b =120 sq metres and a perimeterequals: P = 2a + 2b =46 metres (2) a + b = P/2 =23 The length of itsdiagonal is: l^2 = a^2 + b^2 But, a^2 + b^2 = (a + b)^2 - 2ab Therefore: l^2 = (P/2)^2 - 2S = 23^2 - 2*120 = 289 l = Sqrt[289] = 17 metres Answer: The length of diagonal is 17 metres
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