Aled has three concrete slabs. Two of the slabs are square, with each side of length x metres. The third slab is rectangular and measures 1 metre by (x +1) metres. The three concrete slabs cover an area of 7m^2. Show that 2x^2 + x – 6 = 0. Find x.

For the first part of the question, we can firstly assume that the... area of slab 1 + area of slab 2 + area of slab 3 = total area, which we know to be 7m^2Knowing that to work out the area of a square we use... Area=base^2 and similarly for a rectangle we use Area = base x height.Using these formulae, we can see that... Area of slab 1 = Area of slab 2 = x^2 Area of slab 3 = 1 x (x+1) = x+1Using our first formula .. area of slab 1 + area of slab 2 + area of slab 3 = x^2 + x^2 + x+1 = 7.Simplifying this equation (grouping like terms such as x^2 and remembering the rule that everything we do to one side of the equation, we do to the other side) We get, 2x^2 + x - 6 = 0

For the second part, there are multiple methods for solving the above equation to find x. We could factorise the equation finding 2 brackets, use trial and improvement substituting values for x (least recommended method) or use the quadratic formula (most recommended method). Usually the student will show a preference in which method to use, so I could identify which I think is most beneficial for the student.The quadratic formula (something the students would have to learn) is x=-b+-sqrt(b^2-4ac)/2aWe can look at the coefficients (numbers before the x's) of the equation we wish to solve. So a=2, b=1, c=-6Substituting these into the equation and solving (would use the whiteboard to explain step by step if needed) to getx=-1+-7 / 4 . It is important to remember that lengths have to always be positive, so we can disregard the negative number, leaving us with the answer x= 1.5Sub these in to the question to find the lengths of the slabs.