Unit 2
4 marks · NormalA rectangle has a length of 4x cm and a width of 2x cm. The area of the rectangle is equal to 72 cm².
Write down an equation in terms of x for the area of the rectangle.
Solve your equation to find the value of x.
Calculate the perimeter of the rectangle.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 4x × 2x = 72
(b) x = 3
(c) 30 cm
Common mistakes: Incorrectly multiplying expressions for area; Wrong steps solving the quadratic equation
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Writes a correct algebraic expression for area (4x × 2x = 72 or equivalent)
M2 (b) · 1 mark · Attempts to solve (4x × 2x = 72 ⇒ 8x² = 72)
A1 (b) · 1 mark · x = 3 (accept x = -3 but only take positive solution for length)
A2 (c) · 1 mark · Perimeter correctly calculated as 30 cm (follow-through)
Worked solution
a) Area = length × width ⇒ 4x × 2x = 8x². Set equal to 72: 8x² = 72.
b) Solve: 8x² = 72 ⇒ x² = 9, so x = 3 (since x > 0).
c) Perimeter = 2 × (4x + 2x) = 2 × 6x = 12x. When x = 3, perimeter = 12 × 3 = 36 cm.