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Question
Clearly show the algebraic inequalities that were used and all the necessary work involved in solving the problems. (1)Jenny wants to utilize a portion of her garden for growing flowers. Being a designer herself, she visualizes a triangular area with different lengths for each side. For this Jenny decides to keep a side of the triangular area 5 feet shorter and the other 4 feet longer than the third side. She also wants to restrict the perimeter of the triangular area to 29 feet, so that it does not cover a huge area of the garden. Determine the length of each side of the triangular area that Jenny has visualized. (2)Two graphic artists are working on a 3D game project. One artist works 3 hours more than his colleague. Together they work more than 27 hours. Find the possible number of hours each of them worked.
Clearly show the algebraic inequalities that were used and all the necessary work involved in solving the problems. (1)Jenny wants to utilize a portion of her garden for growing flowers. Being a designer herself, she visualizes a triangular area with different lengths for each side. For this Jenny decides to keep a side of the triangular area 5 feet shorter and the other 4 feet longer than the third side. She also wants to restrict the perimeter of the triangular area to 29 feet, so that it does not cover a huge area of the garden. Determine the length of each side of the triangular area that Jenny has visualized. (2)Two graphic artists are working on a 3D game project. One artist works 3 hours more than his colleague. Together they work more than 27 hours. Find the possible number of hours each of them worked.
Answer
Let one side be x Then 2nd side is (x – 5) 3rd side is (x + 4) Perimeter is sum of 3 sides = x + (x – 5) + (x + 4) = 29 3 x – 1 = 29 3 x = 30, x = 10 Sides are 10, 5, 14 Let one of them work for x hr. then second one works for (x + 3) hr. Total working hours = x + x + 3 = 27 2 x = 24 x = 12 One of them work for 12 and other for 13 hr.
Let one side be x Then 2nd side is (x – 5) 3rd side is (x + 4) Perimeter is sum of 3 sides = x + (x – 5) + (x + 4) = 29 3 x – 1 = 29 3 x = 30, x = 10 Sides are 10, 5, 14 Let one of them work for x hr. then second one works for (x + 3) hr. Total working hours = x + x + 3 = 27 2 x = 24 x = 12 One of them work for 12 and other for 13 hr.
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