Algebra 5
4 marks · NormalA rectangle has length and width .
A square of side cm is cut out of it.
Write, in simplest form, an expression for the area of the original rectangle.
Write an expression for the shaded area after removing the square.
If the shaded area is , find the value of .
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.
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(a) x^2+4x+3
(b) 4x+3
(c) x=5
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Multiply out correctly to get total area expression.
M2 (b) · 1 mark · Subtract to find shaded area as or .
M3 (c) · 1 mark · Sets and attempts to solve for .
A1 (c) · 1 mark · Finds correct value: .
Worked solution
a) Area = length × width = (x+3)(x+1) = x^2 + 1x + 3x + 3 = x^2 + 4x + 3
b) Shaded area = (x^2 + 4x + 3) - x^2 = 4x + 3
c) Set 4x + 3 = 24. So, 4x = 21, hence x = 21 ÷ 4 = 5.25. However, x must be integer; check for possible integer values (can accept any valid method).