Question

John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school?

Answer 1

We must recall the Pythagoras' theorem.

Pythagoras' theorem states that for all right-angled triangles, 'The square on the hypotenuse is equal to the sum of the squares on the other two sides'.

The hypotenuse is the longest side of a right triangle.

Given:

Distance walked by John in the north direction$=8$ blocks

Distance walked by John in the west direction$=6$ blocks

Clearly, these are perpendicular to each other.

Here, Using the Pythagoras' theorem,

$AC^{2} =AB^{2}+BC^{2} \\ \implies AC^{2} =8^{2}+6^{2} \\ \implies AC^{2} =64+36 \\ \implies AC^{2} =100\\ \implies AC =\sqrt{100} \\ \implies AC=10$

Hence the distance between the school and John's home is $10$ blocks

Answer 2

Given,

John walks 6blocks to the North.

Then walks 8blocks to the West.

To Find,

The distance between school and john's position.

Solution,

John is going to the house from the school.

He covered 6block to the North direction.

And traveled 8block to the west direction.

In the given figure,

We need to find the third side of the triangle.

From the Pythagorean theorem,

AC² = AB²+BC²

AC² = 6²+8²

AC² = 36 + 64

AC² = 100

AC = √100.

AC = 10blocks.

Hence, 10blocks is the distance between the school and John.