Question

You ride your bicycle along the outer edge of the park. Then you take a shortcut back to where you started. Find the length of the shortcut. Round your answer to the nearest tenth.

Answer: _______m​

Answer 1

The length of the short cut is approximately 116.62 m.

Step-by-step explanation:

Here we have redraw the diagram with nomenclature for your reference.

Given,

AB = 100 m

BC = 60 m

We have to find out the length of short cut i.e. AC.

Solution,

Since according to the given diagram ∠B is equal to 90°.

So here we apply the Pythagoras theorem to find AC.

"In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides".

On substituting the given values, we get;

Now taking square root on both side, we get;

Hence The length of the short cut is approximately 116.62 m.

Answer 2

The length of the short cut is approximately 116.62 m.

Explanation:

Here we have redraw the diagram with nomenclature for your reference.

Given,

AB = 100 m

BC = 60 m

We have to find out the length of short cut i.e. AC.

Solution,

Since according to the given diagram ∠B is equal to 90°.

So here we apply the Pythagoras theorem to find AC.

"In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides".

`AB^2+BC^2=AC^2`

On substituting the given values, we get;

`AC^2=100^(2)+60^(2)\\ \\AC^2=10000+3600\\\\AC^2=13600`

Now taking square root on both side, we get;

`√(AC^2) =√(13600)\\ \\AC =116.619\approx116.62\ m`

Hence The length of the short cut is approximately 116.62 m.