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

Question 6

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

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Answer

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

$P = 2(l + w)$

Substituting the values for length and width: $46 = 2((4x - 5) + (x + 3))$

Step 2

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Answer

Simplifying the equation:

a) Combine like terms: $46 = 2(5x - 2)$

b) Divide both sides by 2: $23 = 5x - 2$

c) Add 2 to both sides: $25 = 5x$

d) Divide by 5: $x = 5$

Step 3

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Answer

Substituting $x = 5$ back into the expressions for length and width:

Length: $l = 4(5) - 5 = 20 - 5 = 15 ext{ cm}$

Width: $w = 5 + 3 = 8 ext{ cm}$

Step 4

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120 rated

Answer

The area $A$ of a rectangle is calculated using the formula:

$A = l imes w$

Substituting the values: $A = 15 imes 8 = 120 ext{ cm}^2$

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