Question

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?

Answer 1

Answer:

  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.

Answer 2

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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