document.write( "Question 688106: An arch is in the form of a semiellipse. It's 50 metres wide at the base and has a height of 20 metres. How wide is the arch at the height of 10 metres above the base? This is my question please help on the solution, i tried it so many times but i can't gate the clue yet. Help me . \n" ); document.write( "
Algebra.Com's Answer #425705 by lwsshak3(11628)\"\" \"About 
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An arch is in the form of a semiellipse. It's 50 metres wide at the base and has a height of 20 metres. How wide is the arch at the height of 10 metres above the base?
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\n" ); document.write( "Use standard form of equation for an ellipse wit horizontal major axis:
\n" ); document.write( "(x-h)^2/a^2+(y-k)^2/b^2=1, a>b, (h,k)=(x,y) coordinates of center.
\n" ); document.write( "For given problem:
\n" ); document.write( "place center at (0,0)
\n" ); document.write( "a=25
\n" ); document.write( "a^2=625
\n" ); document.write( "b=20
\n" ); document.write( "b^2=400
\n" ); document.write( "Equation: x^2/625+y^2/400=1
\n" ); document.write( "at a height of 20 metres, the coordinates are (x,20)
\n" ); document.write( "plug in these coordinates and solve for x
\n" ); document.write( "x^2/625+y^2/400=1
\n" ); document.write( "x^2/625+10^2/400=1
\n" ); document.write( "x^2/625+100/400=1
\n" ); document.write( "x^2/625=1-1/4=3/4=.75
\n" ); document.write( "x^2=.75*625=468.75
\n" ); document.write( "x=√468.75
\n" ); document.write( "x≈21.65
\n" ); document.write( "2x≈43.3
\n" ); document.write( "At the height of 10 metres above the base, the arch is 43.3 metres wide.
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