An open box is made from a 40 -cm by 50-cm piece of tin by cutting a square from each corner and folding the edges. the area of the resulting base is 1344cm squared. what is the length of the sides of the squares?

The length of the sides of the square is 4cm

The formula for calculating the area of the rectangular base is expressed as:

A = LW

L is the length = 40 - 2x

Width = 50 - 2x

Given that the area of the resulting base is 1344cm, we need to get the length of the sides of the square "x"

1344 = (40-2x)(50-2x)

Factorize the  equation as shown:

(40-2x)(50-2x) = 1344

2000 - 80x - 100x + 4x² = 1344

4x²  -  180x + 2000 - 1344 = 0

4x² - 180x + 656 = 0

On factorizing, the positive value of x is 4. Hence the length of the sides of the square is 4cm

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  4 cm

Step-by-step explanation:

If x is the length of the side of the square (in cm), then the area of the base is ...

  1344 = (40 -2x)(50 -2x)

  336 = (20 -x)(25 -x) . . . . . divide by 4

  336 = x^2 -45x +500

Subtracting 336 gives ...

  x^2 -45x +164 = 0

  (x -41)(x -4) = 0 . . . . . . . factor

  x = 4 . . . . . . . . the dimension must be less than 20

The length of the sides of the squares is 4 cm.

A graphing calculator makes short work of it.

25.2

step-by-step explanation:

2+4x6-8/10= 25.2