Problem 34 Sketch, label, and mark the figu... [FREE SOLUTION] (2024)

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Chapter 1: Problem 34

Sketch, label, and mark the figure or write "not possible" and explain why. An equilateral triangle with perimeter $12 a+6 b$

Short Answer

Expert verified

Each side of the triangle is $4a + 2b$. Sketch an equilateral triangle and label each side accordingly.

Step by step solution

Understand the Problem

An equilateral triangle has all three sides of equal length. We need to determine the length of each side given that the perimeter of the triangle is provided as $12a + 6b$.

Determine the Length of Each Side

Since the perimeter is the sum of all sides and the triangle is equilateral, each side is of equal length. Therefore, each side length is $\frac{12a + 6b}{3} = 4a + 2b$.

Sketch and Label the Triangle

Draw an equilateral triangle and label each side with the length $4a + 2b$. Ensure the triangle has all three sides marked with this length and labeled appropriately.

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Perimeter Calculation

The perimeter is the sum of all the sides of a polygon. In the case of an equilateral triangle, all three sides are equal.
To find the length of each side when the perimeter is known, divide the total perimeter by the number of sides.
Since the perimeter in this problem is given as $12a + 6b$, and an equilateral triangle has three equal sides, we calculate:
The length of each side = \frac{12a + 6b}{3} = 4a + 2b\
This means each side of the triangle is $4a + 2b$ units long.

Length of Sides

To determine the length of each side of an equilateral triangle, start with understanding that each side is the same length.
For a triangle with a perimeter given, find the length by dividing this value by three.
For example, in our problem, the perimeter is $12a + 6b$. So, the length of each side is $\frac{12a + 6b}{3} = 4a + 2b$.
This calculation simplifies the understanding and helps you always find the length of each side accurately for any given perimeter.

Geometry Sketching

Sketching geometric shapes helps understand their properties. For an equilateral triangle:

Draw a triangle with all sides and angles equal.
Label each side with the calculated length (in this example, $4a + 2b$).
Ensure the triangle maintains its equal sides to reflect the nature of an equilateral triangle accurately.

This visualization assists with grasping the concept of equal sides and angles in an equilateral triangle.

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Most popular questions from this chapter

Write the words or the symbols that make the statement true. The geometry tool you use to measure an angle is a $?$Draw and carefully label the figures. Use the appropriate marks to indicateright angles, parallel lines, congruent segments, and congruent angles. Use aprotractor and a ruler when you need to. Complementary angles $\angle A$ and $\angle B$ with $m \angle A=40^{\circ}$Four of the statements are true. Make a sketch or demonstrate each truestatement. For each false statement, draw a counterexample. For every line segment there is exactly one midpoint.For Exercises $27-29,$ draw a clock face with hands to show these times. $$3: 40$$Read each problem, determine what you are trying to find, draw a diagram, andsolve the problem. Freddie the Frog is at the bottom of a 30 -foot well Each day he jumps up 3feet, but then, during the night, he slides back down 2 feet. How many dayswill it take Freddie to get to the top and out?

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Problem 34 Sketch, label, and mark the figu... [FREE SOLUTION] (2024)

Short Answer

Step by step solution

Understand the Problem

Determine the Length of Each Side

Sketch and Label the Triangle

Key Concepts

Perimeter Calculation

Length of Sides

Geometry Sketching

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Decision Maths

Geometry

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Privacy Overview

References