The perimeter of the quadrilateral is 54 inches. Find the lengths of the sides.

Question

sides are x+2,x-5, 2x+1 and x^2-3x

Answer 1

If x=7 (which looks correct), then the 4 sides would have lengths 2, 9, 15 and 28.

 

If we attempt to construct (assemble) a TRIANGLE beginning by taking the two side lengths 15 and 28 as two consecutive sides, then we see that the triangle inequality dictates that the third side would have to be > 13.  

 

Since the two remaining sides a of the proposed quadrilateral sum to 11, one can see that it's impossible to make a convex quadrilateral using the four stated sides--because the quadrilateral's area must exceed that of the triangle, and that triangle isn't even possible.

Answer 2

x + 2 + x - 5 + 2x + 1 + x² - 3x = 54

x² + x - 56 = 0

x² + 8x - 7x - 56 = 0

x(x + 8) - 7(x + 8) = 0

(x - 7)(x + 8) = 0

 

x - 7 = 0

x = 7

 

You can figure out the rest from here!

 

x + 8 = 0

x = -8

This answer is out because we don't measure with negative numbers.