# From the front door of his house, Darren walked 9 yards due east and 12 yards due south. What is the shortest distance, in yards, from Darren’s starting point to where he stopped?

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You mean diagonally?

If he has to walk north then west to go back, it will be 9 + 12 yards which is 21 yards.

If not we can use Pythagorean theorem for this.

a^2 * b^2 = c^2

where

c is longest side

and

a and b are the other two sides

or simply a and b will be yards that Darren walked

and c is the shortest distance.

Let's compute,

9^2 * 12^2 = c^2

81 * 144 = c^2

225 = c^2

in order to cancel the square in the c, we need to get the square root of 225 and c^2

√225 = √c^2

so we have

15 = c

therefore,

Darren can walk

I hope it helps.