Clive leaves and walks 12 km due south from work, turns and walks 16 km west to get to the store.How far would Clive need to walk in a straight line to get back to work?

To solve this problem, we can use the Pythagorean theorem because the path Clive took forms a right triangle. The Pythagorean theorem 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. This can be written as: a² + b² = c².

Here, the distance Clive walked south can be one side of the triangle (a = 12 km), and the distance he walked west can be the second side (b = 16 km). We want to find the hypotenuse (c), which represents the straight-line distance from the store back to work.

So, we substitute the given values into the Pythagorean theorem:

(12 km)² + (16 km)² = c² 144 km² + 256 km² = c² 400 km² = c²

To solve for c, we take the square root of both sides:

c = sqrt(400 km²) c = 20 km

So, Clive would need to walk 20 km in a straight line to get back to work.