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

First, simplify the expression inside the parentheses:

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

This simplifies to:

$46 = 2(5x - 2)$

Now, divide both sides by 2:

$23 = 5x - 2$

Add 2 to both sides:

$25 = 5x$

Now divide by 5:

$x = 5$.

Now, substitute x back into the expressions for length and width:

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

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

The area A of a rectangle is given by:

$A = L imes W$

Substituting the values of length and width:

$A = 15 imes 8 = 120 ext{ cm}^2$