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

6th Edition

ISBN: 9781260673531

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

Publisher: McGraw-Hill Education

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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 48PE

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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.

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Chapter 8.5, Problem 47PE

Chapter 8.5, Problem 49PE

Chapter 8 Solutions

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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.

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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.