Chapter 5: Q16 (page 181)

In Exercises 16-17 a segment joins the midpoints of two sides of a triangle.
Find the values of x and y.

Short Answer

Expert verified

The length of x and y is 3 units and 3 units respectively.

Step by step solution

Step 1. Consider the diagram.

The triangle is shown below:

The line segment joins the midpoints of the triangle sides. Length of sides are $4 y + 2$ and $7 (y - 1)$ . Length of midsegment and base of the triangle are $3 x + 5$ and $12 x - 8$ respectively.

Step 2. Show the calculation.

Line segment passes through the midpoint of the side of the triangle.

Hence,

$\begin{array}{l} 4 y + 2 = 7 (y - 1) \\ 4 y + 2 = 7 y - 7 \\ 3 y = 9 \\ y = 3 units \end{array}$

According to the midsegment theorem, the length of the midsegment is half of the base of the triangle.

Hence,

$\begin{array}{l} 3 x + 5 = \frac{1}{2} (12 x - 8) \\ 3 x + 5 = 6 x - 4 \\ 3 x = 9 \\ x = 3 units \end{array}$

Thus, the length of x is 3 units and y is 3 units.

Step 3. State the conclusion.

Therefore, the length of x and y is 3 units and 3 units respectively.

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In Exercises 16-17 a segment joins the midpoints of two sides of a triangle.
Find the values of x and y.

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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In Exercises 16-17 a segment joins the midpoints of two sides of a triangle.Find the values of x and y.

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

Probability and Statistics

Logic and Functions

Theoretical and Mathematical Physics

Pure Maths

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Exercises 16-17 a segment joins the midpoints of two sides of a triangle.
Find the values of x and y.