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if the length of a rectangle is decreased by 2cm and the width is increased by 6 cm the result will be a square the area of this square will be 64 cm^2 greater than the area of a rectangle find the area

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MrRoyal

The area of the rectangle is 105 square cm

How to determine the rectangle area?

Represent the dimensions of the rectangle with x and y

So, the length of the square would be:

Length = x - 2

Width = y + 6

The areas are then calculated as:

Rectangle = xy

Square = (x -2)(y + 6)

The relationship between the areas is:

(x -2)(y + 6) = 64 + xy

Expand

xy + 6x - 2y - 12 = 64 + xy

This gives

6x - 2y - 12 = 64

Add 12 to both sides

6x - 2y= 76

Divide through by 2

3x - y = 38

By trial by error, we have:

x = 15 and y = 7

The rectangle area is then calculated as:

Rectangle = xy

This gives

Rectangle = 15 * 7

Evaluate

Rectangle = 105

Hence, the area of the rectangle is 105 square cm

Read more about areas at:

https://brainly.com/question/27683633

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