Algebra 5
5 marks · NormalA rectangle has a length of (x+7) cm and a width of x cm. The area of the rectangle is 120 cm².
Write an equation for the area in terms of x and expand the brackets.
Rearrange your equation to the form ax² + bx + c = 0.
Solve the equation for x.
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) x(x+7)=120;\ x^2+7x=120
(b) x^2+7x-120=0
(c) x=8\text{ or }x=-15
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Sets up area expression x(x+7)=120.
M2 (a) · 1 mark · Expands brackets correctly to x^2+7x=120.
M3 (b) · 1 mark · Rearranges to quadratic equation x^2+7x-120=0.
M4 (c) · 1 mark · Factors or uses formula to solve quadratic.
A1 (c) · 1 mark · Finds two solutions, x=8 and x=-15.
Worked solution
a) Area = length × width: x(x+7) = 120
Expand: x² + 7x = 120
b) Rearranged: x² + 7x – 120 = 0
c) Factorise: (x+15)(x-8) = 0, so x = –15 or x = 8
Only positive values are usually accepted for lengths, so x = 8.