# Hulk left home and walked 8 blocks west. Then he turned and walked 6 blocks north. If each block is 500 ft long, how far is Hulk from home?

Oct 26, 2016

Hulk is 5000 feet away from home.

#### Explanation:

According to the Pythagorean theory the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides.

It follows that if we have the length of any two sides of a right-angled triangle, we can determine the length of the third side.

In the above problem, we have the length of the two sides that share the right angle. Hence, adding their squares will give us the square of the hypotenuse (which, in this case is the square of the distance of Hulk from his home). By calculating the square root of the added value, we can find out the distance.

Since each block is $500 f t$ long, Hulk walked $8 \times 500 = 4 , 000$ feet west and $6 \times 500 = 3 , 000$ feet north, and we write the equation:

${x}^{2} = {4000}^{2} + 3 , {000}^{2}$

where $x$ represents the hypotenuse.

Simplifying the equation:

${x}^{2} = 16000000 + 9000000$

${x}^{2} = 25000000 = 25 \times {10}^{6}$

x=sqrt(25xx10^6

$x = 5 \times {10}^{3} = 5000$