Chapter 5.1, Problem 25WE

To determine

To fill: in the blanks with the values of x and y for a given parallelogram.

Answer to Problem 25WE

x = $5$

y = $2$

Explanation of Solution

Given information:

A diagram representing a parallelogram with measure of diagonals being given.

Formula used:

A parallelogram is a quadrilateral in which, the diagonals divide themselves into two equal segments about their point of intersection.

Calculation:

Consider the figure given below.

  

Since, the diagonals divide themselves into two equal segments about their point of intersection.This can be expressed as

  $\overline{KT}\cong \overline{TE}$

  $\overline{DT}\cong \overline{CT}$

Substituting the value of the diagonals based on the figure, the above two equations become,

  $x+2y=9$ ……… (1)

  $2x+y=12$ ……… (2)

Multiplying each term of (2) by 2,

  $4x+2y=24$ ……… (3)

Subtracting (1) from (3), the value of x can be calculated as,

  $\begin{array}{l}4x+2y-x-2y=24-9\\ 3x=15\\ x=5\end{array}$

Substituting the value of x in (1) ,

  $\begin{array}{c}5+2y=9\\ 2y=9-5\\ =4\\ y=2\end{array}$

Thus, $y=2,x=5$