Question

The diagonal of a rectangular filed 135m long is 157m. What is the Width of the field?

Answer 1

To solve this exercise let's make a sketch of the rectangular field first:

The length, width, and diagonal of the rectangular field form a right triangle, to determine the width of the rectangle you can apply the Pythagorean theorem.

This theorem states that the square of the hypotenuse is equal to the sum of the square of the legs of the triangle.

`a^2+b^2=c^2`

The diagonal is the hypotenuse of the triangle, the length is one of the legs "a" and the width is the other leg "b".

Write the theorem for b:

`\begin{gathered} a^2-a^2+b^2=c^2-a^2 \\ b^2=c^2-a^2 \\ \sqrt[]{b^2}=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{c^2-a^2} \end{gathered}`

Replace the expression with c=157 and a=135

`\begin{gathered} b=\sqrt[]{157^2-135^2} \\ b=\sqrt[]{24649-18225} \\ b=\sqrt[]{6424} \\ b=80.149\approx80.15 \end{gathered}`

The width of the field is 80.15 meters.