The hypotenuse of a right triangle is 16 ft long. One leg is 6.6 ft longer than the other leg. Find the lengths of the legs. Round to one decimal place.
x = one legx + 6.6 = other leg The Pythagorean Theorem is a² + b² = c² , where a and b are the legs and c is the hypotenuse (the side across from the right angle} The Pythagorean Theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse. So, here we go. a² + b² = c² {the Pythagorean Theorem} x² + (x + 6.6)² = 16² {substituted the sides into the Pythagorean Theorem} x² + x² + 13.2x + 43.56 = 256 {squared the binomial, (x + 6.6) and squared the 16} 2x² + 13.2x - 212.44 = 0 {combined like terms and subtracted 256 from each side} To solve the quadratic equation for x, graph the equation on the graphing calculator, to identify where thegraph hits the x-axis. That is the value of x.
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