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124. A rectangle has a perimeter of 50 units. The length of the rectangle is 3 units more than twice its width. Find the area of the rectangle.
To solve this problem, follow these steps:

Let the width of the rectangle be 'w' units.
Express the length of the rectangle in terms of 'w'.
Use the perimeter formula to set up an equation.
Solve the equation to find the width 'w'.
Calculate the length of the rectangle using the value of 'w'.
Find the area of the rectangle using the length and width.
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Answer :

Despina

Answer:

see below

Step-by-step explanation:

Let's assume:

  • Width of the rectangle = w units.
  • Length of the rectangle = 3 + 2w units

Now the Perimeter of the rectangle can be calculated by using the formula,

  • Perimeter (rectangle) = 2(length + width)
  • 50 = 2(3 + 2w + w )

Let's solve this equation to find the width 'w':

  • 50 = 2(3 + 3w)

divide both sides by 2:

  • 25 = 3 + 3w

subtract 3 from both sides:

  • 25 - 3 = 3w
  • 22 = 3w

divide both sides by 3:

  • w = 7.33 units

Hence, the width of the rectangle is 7.33 units.

Now,

  • Length of rectangle = 3 + 2w units

We can Calculate the length of the rectangle using the value of 'w'.

  • Length of rectangle = 3 + 2(7.33)
  • Length of rectangle = 3 + 14.66
  • Length of rectangle = 17.66 units.

The area of the rectangle using the length and width:

  • Area (rectangle) = length × width
  • Area (rectangle) = 17.66 × 7.33
  • Area (rectangle) = 129.44 sq units
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Answer:

Step 1: Let the width of the rectangle be 'w' units.

Step 2: Express the length of the rectangle in terms of 'w'.

The length of the rectangle is 3 units more than twice its width. So, the length can be expressed as:

Length = 2w + 3

Step 3: Use the perimeter formula to set up an equation.

The perimeter of a rectangle is given by the formula:

Perimeter = 2(Length + Width)

Substituting the given perimeter (50 units) and the expressions for length and width, we get:

50 = 2(2w + 3 + w)

Step 4: Solve the equation to find the width 'w'.

Simplifying and solving for 'w', we get:

50 = 2(3w + 3)

50 = 6w + 6

44 = 6w

w = 44 / 6

w = 7.33

Step 5: Calculate the length of the rectangle using the value of 'w'.

Length = 2w + 3

Length = 2(7.33) + 3

Length = 14.66 + 3

Length = 17.66

Step 6: Find the area of the rectangle using the length and width.

The area of a rectangle is given by the formula:

Area = Length x Width

Substituting the values of length and width, we get:

Area = 17.66 x 7.33

Area = 129.11

Therefore, the area of the rectangle is 129.11 square units.

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