Abox with no top is to be constructed from a piece of cardboard whose length measures 12 inches more than its width. the box is formed by cutting squares that measure 4 inch on each side from the four corners and then folding up the sides. if the volume of the box 256 in cm^3 what are the dimensions of the piece of cardboard? the height? the width?

Width is 12 inches and height is 4 inches.

Step-by-step explanation:

Let the width of the piece of cardboard be = w inches

Then length is = inches

As given, 4 inch squares are cut from each corner;

So, the width is = inches

Length is = inches

When we are folding the cut portion, that gives the height as = 4 inches

The volume is given by : length x width x height

And volume is given as 256 cubic inches

So,

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or

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We get , ; w = -8(neglect the negative value)

; w = 12 inches

And length = inches

Hence, dimensions are : L = 24 inches ; w = 12 inches and h = 4 inches

We can check by putting these values in equation :

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m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°