Question

A house owner wants to cut a marble slab 240cm long amd 120cm wide to 8 pieces of same size,but with least perimeter.Which of the folowwing can be the size of the marble pieces cut out​

Answer 1

Given :  A house owner wants to cut a marble slab 240cm long and 120cm wide to 8 pieces of same size,  but with least perimeter.

To Find : the size of the marble pieces cut out​

Solution:

A house owner wants to cut a marble slab 240cm long and 120cm wide to 8 pieces of same size,

Area =   240  * 120    

Area  of one piece  = 240 * 120 / 8  = 3600

Square has minimum perimeter for a given area

Hence Size of tile  =  √3600  * 3600  =

60 cm * 60 cm

size of the marble pieces cut out​ = 60 cm * 60 cm

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Answer 2

HELLO DEAR,

GIVEN:- A house owner wants to cut a marble slab 240cm long

and 120cm wide to 8 pieces of same size,but with least

perimeter.Which of the folowwing can be the size of

the marble pieces cut out.

SOLUTION:-The dimension of big marble is (240 cm × 120 cm)

We have to cut in 8 piece and the perimeter should

be least of each perimeter.

The least perimeter is only possible in square .

So, according to question

Area of big marble = $\large{240cm×120cm}$

= $\large{28800\:cm^2}$

And the area is divided into 8 part.

So,

=$\large{\frac{28800\:cm^2}{8}}$

= $\large{3600\:cm^2}$

Here area of each tile = $\large{3600\:cm^2}$

And the each tile is a square shape,

So, it's length and breath is same.

Therefore, by using the formula

area of square = $\large{a^2}$

where $\large{a}$ is length of each side.

So, $\large{a^2}$ = $\large{3600\:cm^2}$

$\large{a}$ = $\large{3600^-1/2\:cm^2}$

$\large{a}$ = $\large{60\:cm}$

Therefore size of each marble is $\large{60\:cm}$

THANKS.