Chapter 10: Q12. (page 374)

$\bar{A U,} \bar{B V}$ and $\bar{C W}$ are the medians of $Δ A B C$
If ${AP=x}^{2} and PU = 2x, then x=?$

Short Answer

Expert verified

The value of $x$ is $4$ .

Step by step solution

Step 1. Given information.

$\bar{A U}, \bar{B V}$ and $\bar{C W}$ are the medians of $Δ A B C$ ; $A P = x^{2}$ and $P U = 2 x$ .

Step 2. Concept Used.

Medians divide the midpoint in the ratio $2 : 1$ from the vertex to the side.

Step 3. Let’s calculate the area & height of the rectangle.

Medians divide the midpoint in the ratio $2 : 1$ from the vertex to the side.

From this,

Here,

$\begin{array}{l} \frac{A P}{P U} = \frac{2}{1} \\ A P = 2 P U \\ x^{2} = 4 x \\ x = 0 o r x = 4 \end{array}$

Therefore, $x = 0$ is not possible (length can’t be zero), $x = 4$ is the desired value.

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$\bar{A U,} \bar{B V}$ and $\bar{C W}$ are the medians of $Δ A B C$
If ${AP=x}^{2} and PU = 2x, then x=?$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Let’s calculate the area & height of the rectangle.

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AU,¯BV¯and CW¯are the medians ofΔABCIf AP=x2and PU=2x, then x=?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Let’s calculate the area & height of the rectangle.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

$\bar{A U,} \bar{B V}$ and $\bar{C W}$ are the medians of $Δ A B C$
If ${AP=x}^{2} and PU = 2x, then x=?$