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.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3