Question

To get from point A to point B you must avoid walking through a river. To avoid the river, you must walk 7 miles south and 4 miles east. To the nearest mile, how many miles would be saved if it were possible to walk through the river?

Answer 1

Answer:

• 3 miles would be saved.

Step-by-step explanation:

Given that:

• To get from point A to point B you must avoid walking through a river.
• To avoid the river, you must walk 7 miles south and 4 miles east.

To Find:

• To the nearest mile, how many miles would be saved if it were possible to walk through the river?

Finding the distance between point A and B:

By using pythagoras theorem.

(Hypotenuse)² = (Perpendicular)² + (Base)²

• (Hypotenuse)² = 7² + 4²
• (Hypotenuse)² = 49 + 16
• (Hypotenuse)² = 65
• Hypotenuse = √65
• Hypotenuse = 8 (approx.)

∴ Distance between point A and B = 8 miles

Finding the distance travelled:

Total distance = South + East

• Total distance = 7 + 4
• Total distance = 11

∴ Distance travelled = 11 miles

If it were possible to walk through the river,

Miles saved = Distance travelled - Actutal distance

• Miles saved = 11 - 8
• Miles saved = 3

Hence,

• 3 miles would be saved if it were possible to walk through the river.

Answer 2

Given:-

• To get from point A to point B we must avoid walking through a river.

• To avoid the river, we must walk 7 miles south and 4 miles east.

To Find:-

• Miles would be saved if it were possible to walk through the river.

Theorem used:-

• ${\boxed{Pythagoras \:theorem:-(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2}}$

Solution:-

By using pythagoras theorem,

(Hypotenuse)² = (Perpendicular)² + (Base)²

(AB)² = (AC)² + (BC)²

Here,

• Perpendicular (AC) = 7

• Base (BC) = 4

Putting values,

$:\implies\:(AB)^2 = 7^2 + 4^2$

$:\implies\:(AB)^2 = 49 + 16$

$:\implies\:(AB)^2 = 65$

$:\implies\:AB = \sqrt{65}$

$:\implies\:AB= 8.06$

${\boxed{:\implies\:AB = 8}}$

Hence, The Distance between point A and B is 8 miles.

Now,

⟹ Total distance = Walked to (South + East)

⟹ Total distance = AC + BC

⟹ Total distance = 7 + 4

⟹ Total distance = 11 miles

Now,

⟹ Miles saved = Total Distance travelled - Displacement

⟹ Miles saved = (AC + BC) - AB

⟹ Miles saved = 11 - 8

⟹ Miles saved = 3

Hence, 3 miles would be saved if it were possible to walk through the river.

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