A Fence Problem

Geometry Level 3

A man has a square field, 60 feet by 60 feet, with other property, adjoining the highway. For some reason he put up a straight fence in the line of the three trees, as shown, and the length of fence from the middle tree to the tree on the road was just 91 feet. What is the distance in exact feet from the middle tree to the gate on the road?


The answer is 35.

View wiki
Niaz Bin Siraj by Niaz Bin Siraj , 24, Bangladesh

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Niaz Bin Siraj
May 21, 2015

2 Helpful 1 Interesting 0 Brilliant 4 Confused

Moderator note:

Can you explain how you arrived to the figure above?

Remember the Pythagorean Theorem. The length of fence from the middle tree to the tree on the road is 91 means the Hypotenuse is 91. Now you have to find the length of Base and Perpendicular. As I said the answer was in "EXACT FEET", the square of 91 is found to be the sum of two squares in only one way- the squares of 84 and 35. Actually, (35,84,91) is the only Pythagorean triplet that contain 91.

Niaz Bin Siraj - 6 years ago

Log in to reply

I inputed 36, what :P

Bob Yang - 5 years, 10 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...