Question

Isabelle is using a square piece of cardboard to make a box without a lid. She cuts 2-inch squares from each corner and folds up the edges. The finished box has a volume of 98 cubic inches. Which equation can be used to find the dimensions of the original cardboard piece?

Answer 1

The dimensions of the cardboard to make a box without a lid is 11 inches by 11 inches.

Explanation:

In this problem, we have that Isabelle is using a square piece of cardboard to make a box without a lid. She cuts 2-inch squares from each corner and folds up the edges. The figure below shows this statement. The finished box has a volume (V) of 98 cubic inches, in other words:

$V=98in^3$

When folding up, we get the box without lip shown in the second figure. So the volume would be:

$V=2xx \\ \\ V=2x^2 \\ \\ But: \\ \\ V=98 \\ \\ Then: \\ \\ 2x^2=98 \\ \\ x^2=49 \\ \\ x=\sqrt{49} \\ \\ x=7in$

Since te cardboard is square, then the side (s) is given by:

$s=2+x+2 \\ \\ s=2+7+2 \\ \\ s=11in$

Therefore:

The dimensions of the cardboard to make a box without a lid is 11 inches by 11 inches.

Learn more:

Volume of a box: brainly.com/question/10501080

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Answer 2

Answer:

2(w-4)^2

Step-by-step explanation:

the equation, my explanation is i got it off of imagine math.