IDNStudy.com, ang iyong mapagkukunan ng eksaktong at maaasahang mga sagot. Alamin ang mga maaasahang sagot sa iyong mga tanong mula sa aming malawak na kaalaman sa mga eksperto.
Sagot :
Uncut piece of cardboard:
Width: x inches
Length: 2x inches
Piece of cardboard with four cut-out corners:
Subtract 2 × 2 inches from length and width to compute for the volume of the box.
Width: x - 4 inches
Length: 2x - 4 inches
Height: 2 inches
Volume: 140 cubic inches
Equation:
Length × Width × Height = Volume
(2x-4) (x - 4) (2) = 140
(2x² - 8x - 4x + 16) (2) = 140
(2x² - 12x + 16) (2) = 140
4x² - 24x + 32 = 140
Quadratic equation, ax² + bx + c = 0
4x² - 24x + 32 - 140 = 0
4x² - 24 - 108 = 0
Solve by factoring:
4 (x² - 6x - 27) = 0
4 (x - 9) (x + 3) = 0
x - 9 = 0 x + 3 = 0
x = 9 x = -3
Choose the positive root x = 9.
The dimensions of the piece of cardboard (uncut) are:
Width: x = 9 inches
Length: 2x = 2(9) = 18 inches
The dimensions are 9 inches and 18 inches.
Check:
(18-4) (9-4) (2) = 140
(14) (5) (2) = 140
140 = 140
Width: x inches
Length: 2x inches
Piece of cardboard with four cut-out corners:
Subtract 2 × 2 inches from length and width to compute for the volume of the box.
Width: x - 4 inches
Length: 2x - 4 inches
Height: 2 inches
Volume: 140 cubic inches
Equation:
Length × Width × Height = Volume
(2x-4) (x - 4) (2) = 140
(2x² - 8x - 4x + 16) (2) = 140
(2x² - 12x + 16) (2) = 140
4x² - 24x + 32 = 140
Quadratic equation, ax² + bx + c = 0
4x² - 24x + 32 - 140 = 0
4x² - 24 - 108 = 0
Solve by factoring:
4 (x² - 6x - 27) = 0
4 (x - 9) (x + 3) = 0
x - 9 = 0 x + 3 = 0
x = 9 x = -3
Choose the positive root x = 9.
The dimensions of the piece of cardboard (uncut) are:
Width: x = 9 inches
Length: 2x = 2(9) = 18 inches
The dimensions are 9 inches and 18 inches.
Check:
(18-4) (9-4) (2) = 140
(14) (5) (2) = 140
140 = 140
Pinahahalagahan namin ang bawat tanong at sagot na iyong ibinabahagi. Huwag kalimutang bumalik at magtanong ng mga bagong bagay. Ang iyong kaalaman ay mahalaga sa ating komunidad. May mga katanungan ka? Ang IDNStudy.com ang may sagot. Bisitahin kami palagi para sa pinakabagong impormasyon.
