Explanation Given Information: The provided relationship “the area of an equilateral triangle varies directly as the square of the length of the sides and for an equilateral triangle with 7 cm sides the area is 21.22 cm 2 ”. Formula used: To finding a variational constant k the following steps are written below, Step 1. Write a general variation model that relates the variables given in the problem. Let k represent the constant of variation. Step 2. Solve for k by substituting known values of the variables into the model from step 1. Step 3. Substitute the value of k in the variational model obtained in step 1 to obtain the specific variational model. Step 4. Substitute the value of the known values to obtain the unknown using the variational model obtained in step 3. And, Definition of direct variation is, For a non-zero real constant number k . Then, The y varies direct as x , y ∝ x Then, the y varies directas x , y = k x Calculation: Consider A cm 2 be the area of the equilateral triangle of sides of length x cm therefore A is directly proportional to x . Definition of direct variation is, For a non-zero real constant number k . Then, The A varies directly as the square of x , A ∝ x 2 Then, the A varies directly as the square of x , A = k x 2 Given that for an equilateral triangle with 7 cm sides the area is 21.22 cm 2 . Substitute the variable value, 21.22 = k × 7 2 Now to isolate k divide both side by 7 2 , 21.22 7 2 = k × ( 7 2 ) 7 2 Now Simplify it, 21

4th Edition

ISBN: 9780073384511

Author: Julie Miller, Molly O'Neill, Nancy Hyde

Publisher: MCGRAW-HILL HIGHER EDUCATION

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 8.5, Problem 56PE

To determine

To calculate: The area of an equilateral triangle with 17 cm sides where the area of an equilateral triangle varies directly as the square of the length of the sides and for an equilateral triangle with 7 cm sides the area is 21.22 cm².

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.5, Problem 55PE

Chapter 8.5, Problem 57PE

Chapter 8 Solutions

Beginning and Intermediate Algebra

Ch. 8.1 - Find the domain and range of the relation. { ( 0 ,...Ch. 8.1 - Prob. 2SP Ch. 8.1 - Prob. 3SP Ch. 8.1 - Prob. 4SP Ch. 8.1 - Prob. 5SP Ch. 8.1 - Prob. 6SP Ch. 8.1 - Prob. 7SP Ch. 8.1 - The linear equation, y = − 0.014 x + 64.5 , for...Ch. 8.1 - The linear equation, y = − 0.014 x + 64.5 , for...Ch. 8.1 - The linear equation, y = − 0.014 x + 64.5 , for...

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The area of an equilateral triangle with 17 cm sides where the area of an equilateral triangle varies directly as the square of the length of the sides and for an equilateral triangle with 7 cm sides the area is 21.22 cm 2 .

Solution Summary: The author explains how to find a variational constant k by substituting known values of the variables into the model.

Concept explainers

Videos

To calculate: The area of an equilateral triangle with 17 cm sides where the area of an equilateral triangle varies directly as the square of the length of the sides and for an equilateral triangle with 7 cm sides the area is 21.22 cm².

Want to see the full answer?

Chapter 8 Solutions

The area of an equilateral triangle with 17 cm sides where the area of an equilateral triangle varies directly as the square of the length of the sides and for an equilateral triangle with 7 cm sides the area is 21.22 cm 2 .

Solution Summary: The author explains how to find a variational constant k by substituting known values of the variables into the model.

Concept explainers

Videos

To calculate: The area of an equilateral triangle with 17 cm sides where the area of an equilateral triangle varies directly as the square of the length of the sides and for an equilateral triangle with 7 cm sides the area is 21.22 cm2.

Want to see the full answer?

Chapter 8 Solutions

To calculate: The area of an equilateral triangle with 17 cm sides where the area of an equilateral triangle varies directly as the square of the length of the sides and for an equilateral triangle with 7 cm sides the area is 21.22 cm².