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( "
Algebra.Com's Answer #599860 by Alan3354(69443)![]() ![]() You can put this solution on YOUR website! 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? \n" ); document.write( "------------ \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 \n" ); document.write( "-------------- \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 \n" ); document.write( "------------- \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 \n" ); document.write( " |