Question

A football field is 100 yards long and 50 yards wide. How do you find the length of a diagonal of the football field?

Answer 1

Hint: We can solve this question using the shapes concept. We know that a football field is a rectangle. So on diameter it forms a triangle. Using Pythagoras theorem we will find the third side using the two sides we have.

Complete step-by-step solution:
We know that the football field is rectangular. So it will form two right angle triangles. Using this we can solve our question easily.

We can see in the figure it has formed two right angle triangles.
If \[a,b,c\] are three sides of a right angle triangle then the Pythagoras theorem will be like
\[{{a}^{2}}+{{b}^{2}}={{c}^{2}}\]
We use the above formula to solve the question given.
Given that we have a field with
100 yards long and
50 yards wide.
It will look like

From the figure we can write the Pythagoras theorem for our field.
It will look like
\[{{\left( 100 \right)}^{2}}+{{\left( 50 \right)}^{2}}={{c}^{2}}\]
By simplifying it we will get
\[\Rightarrow {{c}^{2}}=10000+2500\]
By adding the terms we will get
 \[\Rightarrow {{c}^{2}}=12500\]
Now we have to apply square root on both sides of the equation. We will get
\[\Rightarrow \sqrt{{{c}^{2}}}=\sqrt{12500}\]
By simplifying we will get
\[\Rightarrow c=111.80\]
From this we can write the length of the diagonal as \[111.80\].

Note: We have to be aware of the statement that in a rectangle a diagonal creates two right angle triangles then it will be easy to solve the problem. Using the above method we can find any side in the field using two other sides given.