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sesenic [268]
3 years ago
12

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

.
Mathematics
1 answer:
aleksandrvk [35]3 years ago
6 0

Answer:

42 meters

Step-by-step 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

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