Question

A rectangular carpet has area 120 square metre and perimeter 46 metres. Find the length of its diagonal

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

Answer 2

L*B=120....(I)
2L+2B=46
L+B=23
B=23-L
PUT THIS VALUE IN (I)
L*(23-L)=120
23L-L^2=120
-L^2+23L-120
L^2-23L+120
L^2-15L-8L+120
(L-15)(L-8)
L=15,8
Now length of diagonal =root((15)^2+(8)^2)
root(225+64)=root(289)=17
So length of diagonals =17m