Rectangle ABCD has sides 2x+5 and x+2 with rectangle EFGH of sides x+3 and x cut out of it. The total area of shape ABCD is 5cm^2. Show that 0 = x^2 + 6x +5 [5 Marks]
Area of ABCD = (2x+5)(x+2) = 2x2 +9x +10Area of EFGH = (x+3)(x) = x2 + 3xTotal Area = 5 = ABCD - EFGH = 2x2 +9x +10 - x2 - 3x 5 = x2 + 6x +10 0 = x2 + 6x +5(Follow up question could be to find x, either by factorising above equation or using the quadratic formula)
