Question
2-2 Problems 2) Juan wants to paint his bedroom wall. The length of the wall is 8ft. less than twice its width. If the area of the wall is 192ft^2 what are the dimensions of the wall? Level 3 - 3 Problems
Solution
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(209 Votos)
Jucélia
Mestre · Tutor por 5 anos
Resposta
To solve this problem, we need to find the dimensions of the wall based on the given information.Given information:- The length of the wall is 8ft. less than twice its width.- The area of the wall is 192ft².Let's define the variables:- Let the width of the wall be x ft.- Then, the length of the wall would be 2x - 8 ft.The area of the wall192ft², so we can write the equation:Area = Length × Width192 = (2x - 8) × xNow, we can solve this equation to find the value of x:192 = 2x² - 8x0 = 2x² - 8x - 1920 = 2(x² - 4x - 96)0 = 2(x - 12)(x + 8)The solutions to this equation are:x = 12 or x = -8Since the width cannot be negative, the width of the wall is 12 ft.Now, we can find the length of the wall:Length = 2x - 8Length = 2(12) - 8Length = 24 - 8Length = 16 ftTherefore, the dimensionsWidth = 12 ftLength = 16 ft