At the start of the day, a builder rested a 3 m ladder against a vertical wall so that the foot of the ladder was 70 cm away from the base of the wall. During the day, the ladder slipped down the wall, causing the foot of the ladder to move 50 cm further away from the base of the wall. How far down the wall, in centimetres, did the ladder slip? Give your answer to the nearest 1 cm.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Step 1: Convert all measurements to the same unit. In this case, we'll use centimeters. The ladder is 3 m, which is 300 cm. The initial distance from the wall is 70 cm, and the ladder slipped an additional 50 cm, making the final distance 120 cm.

Step 2: Calculate the initial height of the ladder against the wall. We'll call this height 'a'. We know the length of the ladder (hypotenuse 'c') and the initial distance from the wall (side 'b'). So, we can use the formula a = sqrt(c^2 - b^2) to find 'a'.

a = sqrt((300 cm)^2 - (70 cm)^2) = sqrt(90000 cm^2 - 4900 cm^2) = sqrt(85100 cm^2) = 291.7 cm

Step 3: Calculate the final height of the ladder against the wall after it slipped. We'll call this height 'd'. We know the length of the ladder (hypotenuse 'c') and the final distance from the wall (side 'e'). So, we can use the formula d = sqrt(c^2 - e^2) to find 'd'.

d = sqrt((300 cm)^2 - (120 cm)^2) = sqrt(90000 cm^2 - 14400 cm^2) = sqrt(75600 cm^2) = 275 cm

Step 4: Subtract the final height of the ladder from the initial height to find out how far the ladder slipped down the wall.

Slipped distance = a - d = 291.7 cm - 275 cm = 16.7 cm

So, the ladder slipped approximately 17 cm down the wall.