wxyz is a rectangle and the perimeter of ?xyz = 24. if xy + yz =5x -1 and xz =13 -x, then wy = ?

Question

 wxyz is a rectangle and the perimeter of ?xyz = 24. if xy + yz =5x -1 and xz =13 -x, then wy = ?

Answer 1

Hey Bill.

 

A rectangle has congruent diagonals.  This means that the quantity we are looking for, WY, is the same length as the measurement they gave us,  XZ = 13 - x.

 

Draw this rectangle.  Be sure to label the vertices in the same order they are given in the problem:

 

 W-------------------X

   |                       |

   |                       |

  Z-------------------Y

 

Another useful information they gave you was that XY (a vertical length) + YZ (a horiaontal length) = 5x-1.

 

The other useful information is the Perimeter = 24.   

 

Notice that 1 vertical length + 1 horizontal length is half of the perimeter.

Half of the perimeter is 12, so XY + YZ = 5x-1 =12

 

Solving for x, get  x = (13/5).

 

The diagonal has a measure of 13-x,

 

so 13-(13/5) = (65/5) - (13/5) = (52/5) = 10.4