Question

The area of a rectangle is 192 cm² and its perimeter is 56 cm. Find the dimensions of the rectangle. 

Answer 1

Area of the rectangle  `192 cm^2`

Perimeter of the rectangle 56 cm

Perimeter = 2(length + breath)  

⇒`56=2(l+b)` 

⇒`l+b=28` 

⇒` l=28-b` 

`"Area"="Length" xx "breath"` 

⇒`192=(28-b)xb`  

⇒`192=28b-b^2` 

⇒`b^2-28b+192=0` 

⇒`(b-16) (b-12)=0` 

⇒` b=16  or  12` 

Thus, we have; 

`l=28-12` 

⇒`l=28-12` 

⇒` l=16` 

We will take length as 16 cm and breath as 12 cm because length is greater than breath by convention.