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The figure below is made up of 2 squares, A and B of different sizes.

When Square A is placed over Square B, the area of the uncovered part of Square B is 1920 m2. Find the length of each side of Square A.

The Figure Below Is Made Up Of 2 Squares A And B Of Different Sizes When Square A Is Placed Over Square B The Area Of The Uncovered Part Of Square B Is 1920 M2 class=

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Given Data:

  • The difference in length between the larger square and the smaller square is 24 m.
  • The uncovered area is 1920 m².

Steps to Solve:

   1.   Let the side length of the smaller square be x.

   2.  Then, the side length of the larger square will be x + 24 m.

   3. Calculate the area of both squares:

                             Area of the smaller square (A) = x²

                             Area of the larger square (B) = (x + 24)²

    4.  Calculate the area of the uncovered region:

         Uncovered area = Area of (larger square − smaller square)=1920m²

    5. Set up the equation:

                                            (x + 24)² − x² = 1920

    6.  Expand and simplify the equation:

                                            x² + 48x + 576 − x² = 1920

                                                       48x + 576 = 1920

     7.  Solve for x :

                                              48x = 1920 − 576

                                                 48x = 1344

                                                    x  = 28m

Conclusion:

  • The side length of the small square A is 28 m.
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