Use The Function Gx=-5x+17 To Answer The Questions - Gauthmath

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Question

The diagram shows a square ABCD and a right-angled triangle PQR with equal areas. Based on the information, form a quadratic equation in terms o x LP4SHOW LESS104

Solution

user avatar imageAnswer\(9x^2 + 4x - 12 = 0\)ExplanationStep 1: Let the side of the square \(ABCD\) be \(3x + 2\). Step 2: The area of the square \(ABCD\) is \((3x + 2)^2\). Step 3: Let the base of the right-angled triangle \(PQR\) be \(4x + 8\). Step 4: The height of the triangle \(PQR\) is given as \(4\). Step 5: Since the areas of the square and the triangle are equal, set up the equation: \[ (3x + 2)^2 = \frac{1}{2} \times 4(4x + 8) \] Step 6: Expand the square and simplify the right side of the equation: \[ 9x^2 + 12x + 4 = 8x + 16 \] Step 7: Rearrange the terms to form a quadratic equation: \[ 9x^2 + 4x - 12 = 0 \] So, the quadratic equation in terms of \(x\) is \(9x^2 + 4x - 12 = 0\).Click to rate:82.4(338 votes)Search questionBy textBy image/screenshotDrop your file here orClick Hereto upload

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