Chapter 5: Q25 (page 170)

Quad. DECK is a parallelogram. Complete.
If $KT = 2 x + y, DT = x + 2 y, TE = 12$ and $TC = 9$ , then $x = ?$ and $y = ?$

Short Answer

Expert verified

The value of x and y is 5 and 2 respectively.

Step by step solution

Step 1. Consider the following diagram.

Step 2. Apply property of parallelogram.

Diagonals of a parallelogram bisect each other, that is, two segments of each diagonal are equal to one another.

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

$\begin{matrix} x + 2 y = 9; \\ 2 x + y = 12 \end{matrix}$

Step 3. Description of step.

Multiply equation $2 x + y = 12$ by 2.

$\begin{matrix} 2 (2 x + y) = 2 \times 12 \\ 4 x + 2 y = 24 \end{matrix}$

Step 4. Description of step.

Subtract $x + 2 y = 9$ from $4 x + 2 y = 24$ .

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

Step 5. Description of step.

Substitute 5 for x into $2 x + y = 12$ to find the value of y.

$\begin{matrix} 2 \times 5 + y = 12 \\ 10 + y = 12 \\ y = 12 - 10 \\ = 2 \end{matrix}$

Therefore, the value of x and y is 5 and 2 respectively.

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Quad. DECK is a parallelogram. Complete.
If $KT = 2 x + y, DT = x + 2 y, TE = 12$ and $TC = 9$ , then $x = ?$ and $y = ?$

Short Answer

Step by step solution

Step 1. Consider the following diagram.

Step 2. Apply property of parallelogram.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Description of step.

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Quad. DECK is a parallelogram. Complete.If KT=2x+y,DT=x+2y,TE=12and TC=9, thenx=? andy=?

Short Answer

Step by step solution

Step 1. Consider the following diagram.

Step 2. Apply property of parallelogram.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Quad. DECK is a parallelogram. Complete.
If $KT = 2 x + y, DT = x + 2 y, TE = 12$ and $TC = 9$ , then $x = ?$ and $y = ?$