Question #27021

A rectangular carpet has an area of 120 sq metres and a perimeter of 46 metres. The length of
its diagonal (in metres) is:

Expert's answer

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

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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