Chapter 5: Q26 (page 170)

$▱ DECK$ is a parallelogram. Complete.
If $DE = x + y, EC = 12, CK = 2 x - y$ and $KD = 3 x - 2 y$ then and $x = ?$ , $y = ?$ , and the perimeter of $▱ DECK$

Short Answer

Expert verified

The value of x and y is 6 and 3 respectively and the perimeter of a $▱ D E C K$ is 42.

Step by step solution

Step 1. Apply property of parallelogram.

Opposite sides of a parallelogram are congruent, that is, they are equal in length.

In a given figure, by the property of a parallelogram,

$\begin{matrix} x + y = 2 x - y \\ x = 2 y; \\ 3 x - 2 y = 12 \end{matrix}$

Step 2. Description of step.

Substitute 2y for x into $3 x - 2 y = 12$ to find the value of y.

$\begin{matrix} 3 (2 y) - 2 y = 12 \\ 6 y - 2 y = 12 \\ 4 y = 12 \\ y = 3 \end{matrix}$

Step 3. Description of step.

Substitute 3 for y into $x = 2 y$ to find the value of x.

$\begin{matrix} x = 2 \times 3 \\ = 6 \end{matrix}$

Step 4. Description of step.

The perimeter of a parallelogram is given by

$\begin{matrix} P = 2 (D E + E C) \\ = 2 (x + y + 12) \\ = 2 (6 + 3 + 12) \\ = 42 \end{matrix}$

Therefore, the value of x and y is 6 and 3 respectively and the perimeter of a $▱ D E C K$ is 42.

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$▱ DECK$ is a parallelogram. Complete.
If $DE = x + y, EC = 12, CK = 2 x - y$ and $KD = 3 x - 2 y$ then and $x = ?$ , $y = ?$ , and the perimeter of $▱ DECK$

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

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▱DECKis a parallelogram. Complete.If DE=x+y,EC=12,CK=2x-yand KD=3x-2ythen and x=?,y=?, and the perimeter of▱DECK

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

$▱ DECK$ is a parallelogram. Complete.
If $DE = x + y, EC = 12, CK = 2 x - y$ and $KD = 3 x - 2 y$ then and $x = ?$ , $y = ?$ , and the perimeter of $▱ DECK$