document.write( "Question 978473: A triangle has sides measuring 13 cm, 13 cm, and 10 cm. A second triangle is drawn with sides measuring 13 cm, 13 cm, and x cm, where x is a whole number other than 10. If the two triangles have equal areas, what is the value of x? Show your work. \n" ); document.write( "
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A triangle has sides measuring 13 cm, 13 cm, and 10 cm. A second triangle is drawn with sides measuring 13 cm, 13 cm, and x cm, where x is a whole number other than 10. If the two triangles have equal areas, what is the value of x?
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\n" ); document.write( "Area = b*h/2
\n" ); document.write( "Sides a = 13, b = 13, c = 10
\n" ); document.write( "Area = b*h/2
\n" ); document.write( "b = 1 of the 13 cm sides.
\n" ); document.write( "Angle C is between the 2 13 cm sides
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\n" ); document.write( "Use the Cosine Law.
\n" ); document.write( "10^2 = 13^2 + 13^2 - 2*13*13*cos(C)
\n" ); document.write( "cos(C) = 238/338
\n" ); document.write( "Angle C =~ 45.2397 degs
\n" ); document.write( "To have the same value of h, angle C' for side x is the supplement of C = 134.76 degs
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\n" ); document.write( "Use the Cosine Law to find x:
\n" ); document.write( "x^2 = 13^2 + 13^2 - 2*13*13*cos(134.76)
\n" ); document.write( "x^2 = 338 + 338*cos(C) = 338 + 238 = 576
\n" ); document.write( "x = 24 cm
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