Question

An open box is made from a 40-cm by 89-cm piece of tin by cutting a square from each corner and folding up the edges. The area of the resulting base is 2100cm^. What is the length of the sides of the square

Answer 1

√365 cm

Explanation:

We can begin by using the formulas for the area of a rectangle and a square to set up an equation. Let x be the length of the sides of the square that is cut out of each corner of the rectangle.

The area of the original rectangle is 40cm * 89cm = 3560cm^2.

The area of the square that is cut out of each corner is x^2.

The area of the remaining base of the box is 2100cm^2.

So, we have:

3560cm^2 - 4x^2 = 2100cm^2

Solving for x, we get:

x = √(3560cm^2 - 2100cm^2)/4 = √(1460cm^2)/4 =√365cm

So the length of the sides of the square is √365 cm

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