Question

If one side of a square is increased by 8 cm and an adjacent side decreased by 2 cm, a rectangle is formed whose perimeter is 40 cm. Find the length of a side of the square?

Answer 1

The original side length of the square is 7 cm. This is calculated by using the given changed dimensions of the rectangle along with the information that the rectangle's perimeter is 40 cm.

Step-by-step explanation:

To find the length of a side of the original square before it was altered into a rectangle, we start by understanding the resulting rectangular dimensions that give a perimeter of 40 cm. Let x represent the original square's side length in cm. If one side of the square is increased by 8 cm, it becomes x + 8 cm. If an adjacent side is decreased by 2 cm, it becomes x - 2 cm. Given these changes, we form a rectangle with a perimeter of 40 cm.

The perimeter of a rectangle is calculated using the formula P = 2l + 2w, where l is the length and w is the width. In this case, the length is x + 8 cm and the width is x - 2 cm, giving us the equation:

40 = 2(x + 8) + 2(x - 2)

Solving for x:

40 = 2x + 16 + 2x - 4

40 = 4x + 12

40 - 12 = 4x

28 = 4x

x = 7

Therefore, the original side length of the square is 7 cm.

Answer 2

Answer: 7 cm

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Step-by-step explanation:

x = side length of the original square (measured in cm).

One side increases by 8 cm to go from x to x+8. At the same time, an adjacent side decreases from x to x-2 (aka it decreases by 2 cm).

The x by x square turns into a x+8 by x-2 rectangle.

L = x+8 = length

W = x-2 = width

P = perimeter of rectangle

P = 2(L+W)

P = 2(x+8+x-2)

P = 2(2x+6)

P = 4x+12

The perimeter of this rectangle is 4x+12, which is set equal to the stated perimeter 40 cm. We'll use this to solve for x.

P = 40

4x+12 = 40

4x = 40-12

4x = 28

x = 28/4

x = 7

The square originally had side lengths of 7 cm.

Increasing this by 8 cm gets us x+8 = 7+8 = 15 cm. So L = 15.

Also, W = x-2 = 7-2 = 5 cm is the width.

Then note how P = 2(L+W) = 2(15+5) = 40 to help confirm the answer.