Question

You have a rectangular sheet 12cm×9cm. What is the side of the largest cube whose net you can cut out of this rectangle.​

Answer 1

Answer:

I think so 9cm will be the answer

Answer 2

Each side of a largest cube that can be cut out from rectangle is 3√2 cm

Step-by-step explanation:

Given as :

The dimension of a rectangle = 12 cm  × 9 cm

The length of rectangle = l = 12 cm

The breadth of rectangle = b = 9 cm

Let The each side of a largest cube that can be cut out = a cm

According to question

∵  Area of rectangle = length × breadth

i.e   Area = l × b

or,  Area = 12 cm × 9 cm

∴   Area of rectangle = 108 cm²

Again

Since a cube is to cut out from rectangle

The Total surface area of a cube = 6 × side²

i.e Total surface area of a cube = 6 × (a cm)²

So,

Area of rectangle = Area of cube

∴    108 cm²  = 6 × (a cm)²

or,   a²  = $\dfrac{108}{6}$

i.e   a²  = 18

∴     a = √18

Or,  a =  3√2  cm

So, Each side of a largest cube that can be cut out = a = 3√2 cm

Hence,  Each side of a largest cube that can be cut out from rectangle is 3√2 cm  Answer