Mercy leaves and walks 6 km due north from the store, turns and walks 8 km west to get to work.How far would Mercy need to walk in a straight line to get back to the store?

To solve this problem, we can use the Pythagorean theorem because the path Mercy 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 Mercy walked north can be one side of the triangle (a = 6 km), and the distance she walked west can be the second side (b = 8 km). We want to find the hypotenuse (c), which represents the straight-line distance from the store to Mercy's work.

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

(6 km)² + (8 km)² = c² 36 km² + 64 km² = c² 100 km² = c²

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

c = √100 km² c = 10 km

So, Mercy would need to walk 10 km in a straight line to get back to the store.