The height of an open box is 1 cm more than the length of a side of its square base. if the open box has a surface area of 96 cm (squared), how do you find the dimensions.?

2 Answers
bp
Sep 11, 2015

The dimensions of the box would be length= width = 4cms and height = 5 cms

Explanation:

Let the side of the square base be x cms, then height would be x+1 cms.

Surface area of the open box, would be area of the base and area of its four faces, =xx +4x*(x+1)

Therefore #x^2 +4x^2 +4x=96#

#5x^2 +4x -96=0#

#5x^2 +24x-20x-96=0#

#x(5x+24) -4(5x+24)=0#
#(x-4)(5x+24)=0#. Reject negative value for x, hence x= 4 cms

The dimensions of the box would be length= width = 4cms and height = 5 cms

Gió
Sep 11, 2015

You'll find #4cm and 5 cm#

Explanation:

Call the length of the side of the square base #x#:
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so:
Surface area #A# is the sum of the areas of the 4 sides plus the area of the base, i.e.:
#A=4[x*(x+1)]+x^2=96#
#4x^2+4x+x^2-96=0#
#5x^2+4x-96=0#
Using the Quadratic Formula:
#x_(1,2)=(-4+-sqrt(16+1920))/10=(-4+-44)/10#
The useful solution will then be:
#x=40/10=4cm#

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