Câu 8: Đa Thúc 3x2-3xy-5x+5y Phân Tích Thành - Gauthmath

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Question

Isosceles trapezoid ABCD is shown with midsegment EF. If base BC=22x , base AD=17x+12 , and EF=18.5x+8 , what is BC? 22 37 44 58SHOW LESS66

Solution

user avatar imageAnswer\(BC = 44\)ExplanationStep 1: Use the formula for the length of the midsegment of a trapezoid, which is \(EF = \frac{BC + AD}{2}\). Step 2: Substitute the given expressions for \(BC\), \(AD\), and \(EF\) into the formula: \(18.5x + 8 = \frac{22x + 17x + 12}{2}\). Step 3: Multiply both sides of the equation by 2 to eliminate the fraction: \(2(18.5x + 8) = 39x + 12\). Step 4: Distribute the 2 on the left side: \(37x + 16 = 39x + 12\). Step 5: Subtract \(37x\) from both sides to get the variable terms on one side: \(16 = 2x + 12\). Step 6: Subtract 12 from both sides to solve for \(x\): \(4 = 2x\). Step 7: Divide both sides by 2 to find the value of \(x\): \(x = 2\). Step 8: Substitute \(x = 2\) back into the expression for \(BC\): \(BC = 22x = 22(2) = 44\). Therefore, \(BC = 44\).Click to rate:91.1(874 votes)Search questionBy textBy image/screenshotDrop your file here orClick Hereto upload

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