Chapter 10: Q5. (page 388)

The medians of $▵ D E F$ are shown. Find the lengths indicated.
$E P = ?$
$P R = ?$
If $F T = 9,$ then $P T = ?$ and $F P = ?$

Short Answer

Expert verified

$E P = 10, P R = 4, F P = 6 .$

Step by step solution

Step 1. Given information:

Medians of triangle $D E F$ are given:

$F T = 9$

Step 2. Concept used:

We use basic geometric and angle concept.

Step 3. Applying the concept:

From the figure, and the theorem $10.4,$

$\begin{array}{l} P S = \frac{1}{3} E S, \\ \Rightarrow E S = E P + P S . \\ Now,if E P = x, \\ E S = x + 5, \\ \Rightarrow 5 = \frac{1}{3} (x + 5), \\ \Rightarrow 15 = x + 5 \\ \Rightarrow x = 10 \\ \Rightarrow E P = 10. \end{array}$

From the figure, and the theorem $10.4,$

$\begin{array}{l} D P = \frac{2}{3} D R, \\ \Rightarrow D R = D P + P R . \\ Now,if P R = y, \\ D R = 8 + y, \\ \Rightarrow 8 = \frac{2}{3} (8 + y), \\ \Rightarrow 24 = 16 + 2 y, \\ \Rightarrow 2 y = 8, \\ \Rightarrow y = 4, \\ \Rightarrow P R = 4. \end{array}$

From the figure, and the theorem $10.4,$ ,

$\begin{array}{l} F P : P T : F T = 2 : 1 : 3. \\ Anditisalsogiventhat F T = 9, \\ \Rightarrow P T : 9 = 1 : 3, \\ \Rightarrow 3 P T = 9, \\ \Rightarrow P T = \frac{9}{3}, \\ \Rightarrow P T = 3. \\ Since F P : 9 = 2 : 3, \\ \Rightarrow F P = \frac{2}{3} \times 9, \\ \Rightarrow F P = \frac{18}{3}, \\ \Rightarrow F P = 6. \end{array}$

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The medians of $▵ D E F$ are shown. Find the lengths indicated.
$E P = ?$
$P R = ?$
If $F T = 9,$ then $P T = ?$ and $F P = ?$

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Concept used:

Step 3. Applying the concept:

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The medians of ▵DEFare shown. Find the lengths indicated.EP=?PR=?If FT=9, then PT=?and FP=?

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Concept used:

Step 3. Applying the concept:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

The medians of $▵ D E F$ are shown. Find the lengths indicated.
$E P = ?$
$P R = ?$
If $F T = 9,$ then $P T = ?$ and $F P = ?$