Three similar pieces of timber of length 240cm, 320cm, are cut into two equal pieces. Find the largest possible area of a square which can be made from any of the three pieces (3m)

You're on a roll — Here is the solution to the timber problem: 1. Three similar pieces of timber of length 240cm, 320cm, are cut into two equal pieces. Find the largest possible area of a square which can be made from any of the three pieces (3m) Step 1: Determine the lengths of the timber pieces after they are cut. Each original piece of timber is cut into two equal pieces. For an original piece of length 240 cm: Length of cut piece_1 = 240 cm2 = 120 cm For an original piece of length 320 cm: Length of cut piece_2 = 320 cm2 = 160 cm The problem implies we have pieces of these lengths available after cutting. Step 2: Calculate the side length of a square that can be made from each type of cut piece. To form a square, four equal sides are needed. The perimeter of the square will be equal to the length of the timber piece used. If s is the side length of the square, then 4s = length of timber piece. For a 120 cm long piece: 4s_1 = 120 cm s_1 = (120)/(4) cm = 30 cm For a 160 cm long piece: 4s_2 = 160 cm s_2 = (160)/(4) cm = 40 cm Step 3: Calculate the area of the square for each case. The area of a square is given by the formula A = s^2. For the square made from a 120 cm piece: A_1 = (30 cm)^2 = 900 cm^2 For the square made from a 160 cm piece: A_2 = (40 cm)^2 = 1600 cm^2 Step 4: Determine the largest possible area. Comparing the two possible areas, 900 cm^2 and 1600 cm^2, the largest possible area is 1600 cm^2. The largest possible area of a square is 1600 cm^2. What's next?