Question

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A farmer bought a field in the shape of a right triangle. The hypotenuse was five miles long, and one leg was four miles long. The road running along the third side was Answer
miles long.

Answer 1

Answer:

The road running along the third side was 3 miles long.

Step-by-step explanation:

Given,

Length of hypotenuse = $5\ mi$

Length of one leg = $4\ mi$

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;

$c^2=a^2+b^2$

Where 'a' = 1st side of right triangle

'b' = 2nd side of right triangle

'c' = hypotenuse

Now we put the given values and get;

$5^2=4^2+b^2\\\\25=16+b^2\\\\b^2=25-16\\\\b^2=9$

Now taking square root on both side, we get;

$\sqrt{b^2} =\sqrt9\\\\b=3\ mi$

Hence The road running along the third side was 3 miles long.