# A rectangular mat has an area of 120 m² and perimeter of 46 The length of its diagonal is :

**Answer: (4) 17 m**

**Solution:-**

Lat the length of the rectangle be L cm and width of the rectangle be B cm.

The area of the rectangular mat = 120

Then L B = 120 …………….. (1)

The perimeter of the rectangular mat = 46

Then, 2 (L + B) = 46

L + B = 46/2

L + B = 23

Square on both side,

(L + B)^2 = 23^2

L^2 + B^2 + 2 x L B = 23 x 23

L^2 + B^2 + 2 x 120 = 529

L^2 + B^2 = 529 – 240

L^2 + B^2 = 289

Square root on both side,

(L^2 + B^2)^1/2 =17

Then, diagonal of the rectangle is 17 cm .

Hence, the correct answer is option (4) 17 cm.