The length of a rectangular picture frame is 3 inches more than 5 times the width. The perimeter is 186 inches. Find the length and the width of the picture frame.
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The length of a rectangular picture frame is 3 inches more than 5 times the width. The perimeter is 186 inches. Find the length and the width of the picture frame.
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Naoma April 5, 2023 в 22:09Let's say the width of the picture frame is x inches. Then, according to the problem, the length is 3 inches more than 5 times the width, which can be written as: Length = 5x + 3 The perimeter of a rectangle is given by the formula: Perimeter = 2 ? (Length + Width) Substituting the values of length and width from above, we get: 186 = 2 ? (5x + 3 + x) Simplifying the expression on the right side, we get: 186 = 2 ? (6x + 3) 93 = 6x + 3 90 = 6x x = 15 Therefore, the width of the picture frame is 15 inches, and the length can be found by substituting x = 15 in the expression we found earlier: Length = 5x + 3 = 5(15) + 3 = 78 So the length of the picture frame is 78 inches.
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