Chapter 5: Q3 (page 192)

For the following figure, $X, Y, Z$ are the midpoints of the sides of isosceles $Δ A B C$ . Name an isosceles trapezoid and find its perimeter.

Short Answer

Expert verified

The trapezoid is $C X Y B$ and the perimeter is 22.

Step by step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

The isosceles trapezoid is a quadrilateral with one pair of parallel lines and one pair of

sides are of equal length.

Consider the triangle $Δ A B C$ .

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

Now,

$\begin{array}{l} \bar{C X} = \frac{A C}{2} = \frac{10}{2} = 5 \\ \bar{B Y} = \frac{A B}{2} = \frac{10}{2} = 5 \\ \bar{Z B} = \frac{B C}{2} = \frac{8}{2} = 4 \\ \bar{C X} = \bar{B Y} = 5 (1) \end{array}$

Thus, $X Y Z B$ is a parallelogram so the opposite sides are equal.

$\begin{array}{l} X Y | | Z B | | C B \\ X Y | | C B \\ X Y = Z B = 4 (2) \end{array}$

Step 3. Step description.

Now, $C X Y B$ has one pair of parallel lines and one pair of equal sides.

So $C X Y B$ is the isosceles trapezoid.

Calculate the perimeter of $C X Y B$ as follows:

$\begin{array}{l} = C X + X Y + B Y + B C \\ = 5 + 4 + 5 + 8 \\ = 22 \end{array}$

Therefore, the perimeter of the trapezoid $C X Y B$ is 22 units.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For the following figure, $X, Y, Z$ are the midpoints of the sides of isosceles $Δ A B C$ . Name an isosceles trapezoid and find its perimeter.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Logic and Functions

Decision Maths

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

For the following figure, X,Y,Zare the midpoints of the sides of isosceles ΔABC. Name an isosceles trapezoid and find its perimeter.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Logic and Functions

Decision Maths

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

For the following figure, $X, Y, Z$ are the midpoints of the sides of isosceles $Δ A B C$ . Name an isosceles trapezoid and find its perimeter.