Question

The perimeter of a rectangle is 82m and its area is  `400m^2` . The breadth of the rectangle is 

(a) 25m                (b)20m    

(c) 16m                 (d)9m

Answer 1

(c) 16 m  

Let the length and breadth of the rectangle be l and b.

Perimeter of the rectangle 82m 

⇒`2xx(l+b)=82` 

⇒ `l+b=41` 

⇒`l=(41-b)`                     ................(1) 

Area of the rectangle  =`400m^2` 

⇒`lxxb=400m^2` 

⇒`(41-b)b=400 `                (using 1) 

⇒`41b-b^2=400` 

⇒`b^2-41b+400=0` 

⇒`b^2-25b-16b+400=0` 

⇒`b(b-25)-16(b-25)=0` 

⇒`(b-25)  (b-16)=0` 

⇒`b=25  or b=16` 

`If b=25  or  b=16` 

`l=41-25=16` 

Since, l cannot be less than b, 

∴`b=16m`