A Rectangular Carpet Has An Area Of 120 Square Meters And Perimeter Of 46m The Length Of Its Diagonal Is:

A rectangular carpet has an area of 120 square meters and perimeter of 46m The length of its diagonal is:

11m
13m
17m
None of these

Explanation

17m

Area of the rectangular carper $= 120 c m^{2}$
Perimeter $= 46 m$
$2 (l + b) = 46$
$(l + b) = 46 / 2$
$l + b = 23$

And, length $\times$ breadth $= 120$
Now, we know that :
$(l - b)^{2} = (l + b)^{2} - 4 l b$
$(l - b)^{2} = (23)^{2} - 4 \times 120$
$(l - b)^{2} = 529 - 480$
$(l - b)^{2} = 49$
$(l - b)^{2} = (7)^{2}$

Hence, $l - b = 7$
And $l + b = 23$

By adding, we get $2 l = 30$
$l = 30 / 2$
$l = 15$

and, $b = 23 - 15$
$b = 8$

Diagonal $= (l^{2} + b^{2})$
$= (15)^{2} + (8)^{2}$
$= (225 + 64)$
$= (289)$
$= 17 m$

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