Math Problem Statement

A rectangular piece of sheet metal has the width 50 ๐‘๐‘š shorter than its length. From each corner, a 10 ๐‘๐‘š ร— 10 ๐‘๐‘š square is cut out and the flaps are then folded up to form an open box. If the volume of the box is 104000 ๐‘๐‘š3, find the length and width of the original piece of sheet metal.

Solution

Let the length of the original piece of sheet metal be LL cm, and the width be WW cm.

We know:

  1. W=Lโˆ’50W = L - 50 (The width is 50 cm shorter than the length).
  2. From each corner, a 10 cm ร— 10 cm square is cut out, and the flaps are folded up to form an open box.
  3. The volume of the box is

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of 3D Shapes
Algebra

Formulas

Volume of a rectangular box: V = L ร— W ร— H
Quadratic equation formula: ax^2 + bx + c = 0

Theorems

Quadratic formula

Suitable Grade Level

Grades 9-11

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