Asked by Shay
Dimensions of a Box A box is made from a rectangular piece of metal with length 50 inches and width 40 inches by cutting out square corners of length x and folding up the sides.
(a) Write an expression that gives the surface area of the inside of the box.
(b) If the surface area of the box is 1900 square inches, find x.
(a) Write an expression that gives the surface area of the inside of the box.
(b) If the surface area of the box is 1900 square inches, find x.
Answers
Answered by
Reiny
No top ?
So I see a base which is (50-2x) by (40-2x)
and I see a height of x
total surface area
= (50-2x)(40-2x) + 2x(50-2x) + 2x(40-2x)
=2000 - 180x + 4x^2 + 100x - 4x^2 + 80x - 4x^2
= -4x^2 + 2000
-4x^2 + 2000 = 1900
-4x^2 = -100
x^2 = 25
x = √25 = 5
check my arithmetic
So I see a base which is (50-2x) by (40-2x)
and I see a height of x
total surface area
= (50-2x)(40-2x) + 2x(50-2x) + 2x(40-2x)
=2000 - 180x + 4x^2 + 100x - 4x^2 + 80x - 4x^2
= -4x^2 + 2000
-4x^2 + 2000 = 1900
-4x^2 = -100
x^2 = 25
x = √25 = 5
check my arithmetic
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