Chapter 5: Q4 (page 180)

Points A, B, E and F are midpoints of $\bar{X C}, \bar{X D}, \bar{Y C}$ and $\bar{Y D}$ . Complete.
If $CD = 8 x$ , and $AB = 3 x + 2$ then $x =$ ? .

Short Answer

Expert verified

$x = 2$

Step by step solution

Step 1. Consider the diagram.

Here, A, B, E and F are the midpoints of sides $\bar{X C}, \bar{X D}, \bar{Y C}$ and $\bar{Y D}$ respectively.

And $C D = 8 x$ and $A B = 3 x + 2$ .

Step 2. Show the calculation.

Consider the triangle $△ X C D$ .

Here, points A and B are the midpoints of $\bar{X C}$ and $\bar{X D}$ .

So, by theorem 5-11 part (2), the side $\bar{A B}$ is half as long as the third side $\bar{C D}$ .

$A B = \frac{1}{2} C D$ …… (1)

Substitute $C D = 8 x$ and $A B = 3 x + 2$ .

$\begin{matrix} A B = \frac{1}{2} C D \\ 3 x + 2 = \frac{1}{2} (8 x) \\ 3 x + 2 = 4 x \\ 2 = 4 x - 3 x \\ 2 = x \end{matrix}$

Step 3. State the conclusion.

Therefore, $x = 2$ .

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Points A, B, E and F are midpoints of $\bar{X C}, \bar{X D}, \bar{Y C}$ and $\bar{Y D}$ . Complete.
If $CD = 8 x$ , and $AB = 3 x + 2$ then $x =$ ? .

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

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Points A, B, E and F are midpoints of XC¯,XD¯,YC¯and YD¯. Complete.If CD=8x, andAB=3x+2 then x= ? .

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Points A, B, E and F are midpoints of $\bar{X C}, \bar{X D}, \bar{Y C}$ and $\bar{Y D}$ . Complete.
If $CD = 8 x$ , and $AB = 3 x + 2$ then $x =$ ? .