Answer to Question #27021 in Geometry for sarang

Question

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

Answer 1

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