Answer:
The road running along the third side was 3 miles long.
Step-by-step explanation:
Given,
Length of hypotenuse = [tex]5\ mi[/tex]
Length of one leg = [tex]4\ mi[/tex]
We have to find the length of the third side.
Solution,
Since the field is in the shape of a right triangle.
So we use the Pythagoras theorem to find the length of the third side.
"In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of other two sides".
On framing in equation form, we get;
[tex]c^2=a^2+b^2[/tex]
Where 'a' = 1st side of right triangle
'b' = 2nd side of right triangle
'c' = hypotenuse
Now we put the given values and get;
[tex]5^2=4^2+b^2\\\\25=16+b^2\\\\b^2=25-16\\\\b^2=9[/tex]
Now taking square root on both side, we get;
[tex]\sqrt{b^2} =\sqrt9\\\\b=3\ mi[/tex]
Hence The road running along the third side was 3 miles long.
