156 inches is the shortest distance to dig diagonally through dirt to get to his family.
<u>Step-by-step explanation:</u>
- A bug dug 60 inches straight down below ground.
- Then continued digging 144 inches parallel to the ground.
This forms the angle 90° between the two lines.
After he realized to turn back., the shortest distance is to dig diagonally.
This forms the hypotenuse side of the triangle.
Therefore, the given data can be assumed as a right angled triangle.
<u>To find the diagonal path (hypotenuse) :</u>
Use the Pythagorean triplets for right angle triangle,
We know that the triplet is (5,12,13).
- It is given that, the height is 60 inches ⇒ 5 × 12
- The base is of 144 inches ⇒ 12 × 12
Therefore, the third side hypotenuse must also be a multiple of 12.
From the triplets (5,12,13), the hypotenuse is 13 and it is multiplied by 12.
Diagonal path ⇒ 13 × 12 = 156 inches.
∴ 156 inches is the shortest distance to dig diagonally through dirt to get to his family.
