An open box is made from a 20-cm by 50-cm piece of tin by cutting a square from each corner and folding up the edges. The area of the resulting base is 216 cm2. What is the length of the sides of the squares?

Therefore,

The length of the sides of the squares is

Step-by-step explanation:

Let "x" be the length of Cut Square,

As the tin size(Dimension) is

20 cm × 50 cm

So the size(Dimension) of box will be

(20 - 2x) × (50 - 2x)

Length = 50 - 2x

Width = 20 - 2x

Area of base of box = 216 cm²

To Find:

x = ?

Solution:

Area of Rectangular field is given by

Substituting the values we get

Applying Distributive property we get

Dividing throughout by 4 we get

On Factorizing we get

As x cannot be 28 because tin size is 20 cm × 50 cm i.e longer than 20

Therefore,

Therefore,

The length of the sides of the squares is

7 cm

Step-by-step explanation:

(20-2x)(50-2x) = 216

4x² - 40x - 100x + 1000 - 216 = 0

4x² - 140x + 784 = 0

x² - 35x + 196 = 0

x² - 28x - 7x + 196 = 0

x(x - 28) - 7(x - 28) = 0

(x - 7)(x - 28) = 0

x = 7, 28

x can not be more than 10 because the dimensions are 20×50

So x = 7 cm

picture below

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i