Question

Starting at home, Brenda walked 1 block north, 2 blocks east, 3 blocks south, 4 blocks west, and so on, each time turning 90 degrees to her right and walking one block further. After walking a total of 190 blocks, how many blocks is Brenda fromhome? Express your answer in simplest radical form.

Answer 1

Brenda will be
`10*√(2)` blocks away from home.

Explanation:

First, let's determine the number of sides to her walk.

`1+2+3+4+.....+19=190`

So, there are 19 segments from 1 to 19

.

The first four points are at (0,0) (0,1) (2,1) and (2,-2) - Let's call these corners SW, NW, NE, and SE respectively.

There are 19 segments, so 1 short of 5 complete laps. If a complete lap begins and ends at the SW corner, (0,0) her home, then the opposite of that is the SE corner. She'll reach 190 blocks on her 5th time.

Starting with the four coordinates for the corners above, note that each lap pushes these corner out 2 squares in each direction, so the SE corner will have the following coordinates for each of the 5 laps:

Lap 1: (2,-2)

Lap 2: (4, -4)

Lap 3: (6, -6)

Lap 4: (8, -8)

Lap 5: (10, -10)

Then the coordinates for 5th lap are (0,0) (0, -10) (-10,0) and (10, -10)

thus solving while taking the hypotenuse of right triangle formed by (0,0) (0,-10) (10,-10)

which gives

`perpendicular=10 \ base=10\\`

So,

`hypotenuses^2=Perpendisuler^2+Base^2`

`h^2=10^2+10^2`

`h^2=200`

`h=10*√(2)`

So, Brenda will be
`10*√(2)` blocks away from home.