Arectangular piece of sheet metal has a length that is 88 in. less than twice the width. a square piece 44 in. on a side is cut from each corner. the sides are then turned up to form an uncovered box of volume 968968 in. cubed. find the length and width of the original piece of metal.

Step-by-step explanation:

Let L and b be the Length and breadth of Rectangular Piece of sheet metal

also

Square piece of 44 in. is cut from each corner

thus New length of cuboid is

Breadth of Cuboid

Height of breadth is

Volume of Cuboid

substitute the value of L i n volume

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)

1st integer x

2nd integer x+1

3rd integer x+2

4th integer x+3

x+x+1 +x+2+x+3 =74

combine like terms

4x+6 = 74

subtract 6 from each side

4x = 68

x = 17

the integers are 17,18,19,20