# If the perimeter and the diagonal of a rectangle is 18 cm and √41 cm respectively.Calculate the area of the rectangular field ?

If the perimeter and the diagonal of a rectangle is 18 cm and √41 cm respectively. Calculate the area of the rectangular field ?

A. 25 cm^{2}

B. 29 cm^{2}

C. 18 cm^{2}

D. 20 cm^{2}

**Answer : **D. 20 cm^{2}

## Explanation:

**Perimeter of rectangle = 18 cm**

2 ( l + b ) = 18 cm

l + b = 18 / 2

= 9 cm

l + b = 9 cm

**Diagonal of rectangle = √41 cm**

We know that, Diagonal of rectangle = √ [ ( length )^{2} + ( breadth )^{2} ]

√( l^{2} + b^{2}) = √41

l^{2} + b^{2} = ( √41 )^{2}

l^{2} + b^{2} = 41

l^{2} + b^{2} + 2 lb - 2 lb = 41

( l + b )^{2} - 2 lb = 41

Since , we have **l + b = 9 **, so now

( 9 )^{2} - 2 l b = 41

81 - 2 lb = 41

2 lb = 81 - 41

2 lb = 40

lb = 40 / 2 = 20 cm ^{2}

l × b = 20 cm^{2}

Therefore, **area of rectangular field = 20 cm ^{2}**