How do I solve for the missing length vector

Question

A farmer builds three sections of a fence, as shown in the figure, where L= 10.00m, and gets tired. Walking straight back to where he started, how far did he have to go? Solve for d the missing side. 

Picture:

https://d2vlcm61l7u1fs.cloudfront.net/media/582/582e08db-c0eb-490c-8424-d8eab5a9f768/phpkkEYWu.png

Answer 1

Hi Eamon R.,

When you have a complex figure such as this you always try to transform it into something simpler!

In this case, draw the rectangle in the lower left corner, leaving a right triangle with hypotenuse L and one side L/2. You should recognize this as a privileged triangle, 30-60-90 degree angles, and you should be able to immediately use memorized ratios (or, with Pythagorean theorem) to obtain L*3^0.5/2 as the other side. Then add the two segments on the left (L *(1+3^0.5/2)) and calculate your answer (if that is what your course demands).

-- Cheers, -- Mr. d.