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A different angle (Posted on 2003-10-10) Difficulty: 3 of 5
Look at this shape:

Assume AB = AF = FE = ED and BC = CD, and all the angles in the shape are 90 degrees.

Let A be the area of this shape (in cm^2), and P -- the perimeter of this shape (in cm).

If A - P is 60, what is the length of line AC?

See The Solution Submitted by Lewis    
Rating: 1.9167 (12 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips re: A different angle | Comment 4 of 23 |
(In reply to A different angle by Callum)

First, when you came up with a negative value for the length, that should have been a sign that something is wrong.
The problem with your anaysis is, the ratio of A to P is not simply 3/8, it is 3/8 times whatever ab is (or af, de, etc). Then, you would have to "times the area and perimeter" 6, instead of -12, to get the equation 104-48=60, which is equal on each side (in essence, you were trying to solve 3x-8x=60 instead of 3x²-8x=60, which is why you got a negative answer). Once you have the right value for x, the Pythagorean theorem gives AC²=6²+12²=180, so AC is about 13.416.
  Posted by DJ on 2003-10-10 09:31:00

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