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Alexeev081 [22]
3 years ago
8

The perimeter of a rectangle is 30 cm. If one of its sides is decreased by 3 cm and the other side is increased by 5 cm, the are

a of the rectangle will decrease by 8 cm2. Find the area of the original rectangle.
Mathematics
1 answer:
jek_recluse [69]3 years ago
7 0

Answer:

Step-by-step explanation:

Let L represent the length of the original rectangle.

Let W represent the width of the original rectangle.

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

The perimeter of a rectangle is 30 cm. This means that

2(L + W) = 30

Dividing through by 2,

L + W = 15

The area would be LW

If one of its sides is decreased by 3 cm and the other side is increased by 5 cm, the area of the rectangle will decrease by 8 cm2. This means that

(L - 3)(W + 5) = LW - 8

LW + 5L - 3W - 15 = LW - 8

LW - LW + 5L - 3W = - 8 + 15

5L - 3W = 7 - - - - - - - - - - - 1

Substituting L = 15 - W into equation 1, it becomes

5(15 - W) - 3W = 7

75 - 5W - 3W = 7

- 5W - 3W = 7 - 75

- 8W = - 68

W = - 68/- 8 = 8.5

L = 15 - W = 15 - 8.5

L = 6.5

The area of the original rectangle is

6.5 × 8.5 = 55.25 cm²

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The original quantity is 20 and the new quantity is 15. Adam incorrectly says the percent decrease is about ​14.29%. What is the
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Answer: A. divided the difference of the two quantities by the sum of the two quantities.

===================================================

Explanation:

The difference of the quantities is 20-15 = 5

The sum of the quantities is 20+15 = 35

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This is likely the path Adam took. This path is incorrect. The correct steps are shown below

---------------------

Difference = 20-15 = 5

Divide the difference over the original quantity

5/20 = 1/4 = 0.25 = 25%

We have a 25% decrease because the new quantity (15) is smaller than the old quantity (20)

----------------------

Here's another way to approach the problem

A = old value = 20

B = new value = 15

C = percent change

C = [ (B-A)/A ] * 100%

C = [ (15-20)/20 ] * 100%

C = (-5/20)*100%

C = -0.25*100%

C = -25%

The negative C value means we have a negative percent change, ie we have a percent decrease. So this is another way to get a 25% decrease.

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