# SOLUTION: The width of a rectangular gate is 2 meters (m) larger that its height. The diagnoal brace measures square root6m. Find the width and height.

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 Question 203369: The width of a rectangular gate is 2 meters (m) larger that its height. The diagnoal brace measures square root6m. Find the width and height.Answer by stanbon(57361)   (Show Source): You can put this solution on YOUR website! The width of a rectangular gate is 2 meters (m) larger that its height. The diagnoal brace measures square root6m. Find the width and height. ----------------------- Draw a picture of a rectangle. Label the width as (x+2) meters. Label the height as (x) meters. Lsbel the diagonal as sqrt(6) meters. --------------------------------- Use Pythagoras to solve for "x". x^2 + (x+2)^2 = [sqrt(6)]^2 2x^2 + 4x + 4 = 6 2x^2 + 4x -2 = 0 x^2 + 2x -1 = 0 Use the quadratic formula to solve for "x": x = [-2 +- sqrt(4 -4*1*-1]/2 x = [-2 +- sqrt(8)]/2 x = [-1 +- sqrt(2)] Positive solution: x = sqrt(2) - 1 = 0.414 meters (this is the height of the rectangle) x+2 = 2.414 meters (this is the width of the rectangle) ============================================================ Cheers, Stan H.