Question

Fernando followed two diagonal paths, Paths 1 and 2, to get from his house, F, to a neighborhood corner store, C, as shown below.

Answer 1

42 meters

Explanation:

Given

See attachment for complete question

Required

Calculate distance FC

FC is calculated as:

`FC = Path\ 1 + Path\ 2`

Where

`Path\ 1 = FB`

`Path\ 2 = BC`

Considering
`\triangle FEB`, we have:

`FB^2 = FE^2 + BE^2` --- Pythagoras theorem

Where

`FE = FD - BA`

`FE = 22m - 15m`

`FE = 7m`

and

`BE = CD - CA`

`BE = 32m - 8m`

`BE = 24m`

So:

`FB^2 = FE^2 + BE^2`

`FB^2 = 7^2 +24^2`

`FB^2 = 49 +576`

`FB^2 = 625`

Take square roots of both sides

`FB = 25`

So:

`Path\ 1 = 25`

Considering
`\triangle BAC`, we have:

`BC^2 = BA^2 + AC^2` --- Pythagoras theorem

Where:

`BA = 15` and
`AC = 8`

So, we have:

`BC^2 = 15^2 + 8^2`

`BC^2 = 225 + 64`

`BC^2 = 289`

Take square roots of both sides

`BC = 17`

So;

`Path\ 2= 17`

Recall that:

`FC = Path\ 1 + Path\ 2`

`FC = 25 + 17`

`FC = 42`