Question

what is the smallest perimeter a rectangle of area 12 cm cube can have?​

Answer 1

Answer:

14

Step-by-step explanation:

area = lb

4*3 or 6*2 or 1*12

perimeter= 14,16,26

Answer 2

Answer:

The smallest perimeter a rectangle of area $12cm^3$ can have is $14cm$.

Step-by-step explanation:

Given that the area of rectangle $= 12 cm^2$

Area of a rectangle $=$ length * breadth

Perimeter of a rectangle $=2(l*b)$

The factors of $12$ are : $1 , 2 , 3 , 4 , 6 , 12$

We have three cases to consider.

Case I:

If one side of the rectangle is $2cm$, then the other side of the rectangle will be $\frac{12}{2} = 6cm$

Perimeter of this rectangle will be :

$2(2+6) \\= 2*8\\= 16cm$

Case II:

If one side of the rectangle is $4cm$, then the other side of the rectangle will be $\frac{12}{4} = 3cm$

Perimeter of this rectangle will be :

$2(4+3) \\= 2*7\\= 14cm$

Case III:

If one side of the rectangle is $1cm$, then the other side of the rectangle will be $\frac{12}{1} = 12cm$

Perimeter of this rectangle will be :

$2(12+1) \\= 2*13\\= 26cm$

From the three cases, we can say that the smallest perimeter is $14cm$ for the rectangle with sides $4cm$ and $3cm$.