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blsea [12.9K]
2 years ago
14

A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the

flaps are folded upward to form an open box. If the volume of the box is 594 inch to the 3 in​, what were the original dimensions of the piece of​ metal?
Mathematics
1 answer:
Dafna11 [192]2 years ago
6 0

The original dimensions of the metal sheet are 22 inches by 52 inch

<h3>What is volume?</h3>

The volume is defined as the space occupied by any object in three dimensions. For a rectangular box, the volume will be calculated by multiplying the length, width, and height of the object.

If the Width of the metal = x

The length is 30 inches longer than its width= x+30

If Squares with sides 6 in long are cut from the four corners and the flaps are folded.

The length of the pre-folded box =x+30-12=(x+18)inch

The width of the pre-folded box = (x-6-6)inch = (x-12) inch

The height of the flap= 6 inch

The volume of the box = 2400-inch cubed

Volume of a Cuboid = LWH

6(x-12)(x+18)=2400

6x²+36x-1296=2400

6x²+36x-1296-2400=0

6x²+36x-3696=0

6(x-22)(28+x)=0

x-22=0 or x+28=0

Therefore the original dimensions of the metal sheet are 22 inches by 52 inch

The complete question with correct data is given below:-

A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 2400 incubated​what were the original dimensions of the piece of​ metal?

To know more about volume follow

brainly.com/question/46030

#SPJ1

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