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This rectangle has length (4x – 5)cm and width (x + 3)cm - OCR - GCSE Maths - Question 6 - 2017 - Paper 1

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Question 6

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This rectangle has length (4x – 5)cm and width (x + 3)cm. The perimeter of the rectangle is 46cm. Calculate the area of the rectangle.

Worked Solution & Example Answer:This rectangle has length (4x – 5)cm and width (x + 3)cm - OCR - GCSE Maths - Question 6 - 2017 - Paper 1

Step 1

Finding the value of x using the perimeter

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Answer

The formula for the perimeter of a rectangle is given by:

P=2(L+W)P = 2(L + W)

Substituting the values:

46=2((4x−5)+(x+3))46 = 2((4x - 5) + (x + 3))

Simplifying the equation:

  1. Combine the length and width: 4x−5+x+3=5x−24x - 5 + x + 3 = 5x - 2

  2. Substitute back into the perimeter formula: 46=2(5x−2)46 = 2(5x - 2)

  3. Divide both sides by 2: 23=5x−223 = 5x - 2

  4. Add 2 to both sides: 25=5x25 = 5x

  5. Finally, divide by 5: x=5x = 5

Step 2

Calculating the area of the rectangle

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Answer

Now that we have the value of x, we can find the dimensions of the rectangle:

Length: L=4x−5=4(5)−5=20−5=15extcmL = 4x - 5 = 4(5) - 5 = 20 - 5 = 15 ext{ cm}

Width: W=x+3=5+3=8extcmW = x + 3 = 5 + 3 = 8 ext{ cm}

Now, we can calculate the area:

A=LimesW=15imes8=120extcm2A = L imes W = 15 imes 8 = 120 ext{ cm}^2

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