Questions: Praxis Core Academic Skills for I this material to answer the following questions. length of a rectangular tapestry is three times that of its height. Let denote the length and height of the tapestry in meters, respectively. Let A denote the area of the tapestry (in meters squared), and let P denote the length of its perimeter. 18. Which of the following equations represents the area A in terms of h ? A=3 h^2 A=h^2 / 3 A=h^3 A=3 h^3 A=3 h

Praxis Core Academic Skills for I this material to answer the following questions. length of a rectangular tapestry is three times that of its height. Let denote the length and height of the tapestry in meters, respectively. Let A denote the area of the tapestry (in meters squared), and let P denote the length of its perimeter. 18. Which of the following equations represents the area A in terms of h ? A=3 h^2 A=h^2 / 3 A=h^3 A=3 h^3 A=3 h

Transcript text: Praxis Core Academic Skills for I this material to answer the following questions. length of a rectangular tapestry is three times that of its height. Let denote the length and height of the tapestry in meters, respectively. Let A denote the area of the tapestry (in meters squared), and let P denote the length of its perimeter. 18. Which of the following equations represents the area $A$ in terms of $h$ ? $A=3 h^{2}$ $A=h^{2} / 3$ $A=h^{3}$ $A=3 h^{3}$ $A=3 h$

Solution

Solution Steps

To find the equation that represents the area $ A $ of the rectangular tapestry in terms of its height $ h $, we need to use the relationship between the length and height. Given that the length is three times the height, the length can be expressed as $ 3h $. The area of a rectangle is calculated as the product of its length and height. Therefore, the area $ A $ can be expressed as $ A = \text{length} \times \text{height} = 3h \times h = 3h^2 $.

Step 1: Define the Variables

Let $ h $ represent the height of the tapestry in meters. According to the problem, the length $ l $ of the tapestry is three times the height, which can be expressed as: \[ l = 3h \]

Step 2: Calculate the Area

The area $ A $ of a rectangle is given by the formula: \[ A = l \times h \] Substituting the expression for length, we have: \[ A = (3h) \times h = 3h^2 \]

Step 3: Evaluate the Area for a Given Height

For a specific height of $ h = 2 $ meters, we can calculate the area: \[ A = 3(2^2) = 3 \times 4 = 12 \text{ square meters} \]