document.write( "Question 268435: a rhombus has sides of length 10 inches, and the lengths of its diagonals difference by 4 inches . what is the area of the rhombus in square inches ? \n" ); document.write( "
Algebra.Com's Answer #196755 by CharlesG2(834)\"\" \"About 
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a rhombus has sides of length 10 inches, and the lengths of its diagonals difference by 4 inches . what is the area of the rhombus in square inches ?\r
\n" ); document.write( "\n" ); document.write( "diagonal d and diagonal d+4\r
\n" ); document.write( "\n" ); document.write( "rhombus is made of 4 right triangles with the same area\r
\n" ); document.write( "\n" ); document.write( "so using pythagorean theorem on one of the 4:
\n" ); document.write( "the sides of the triangle would be d/2 and (d+4)/2 and hypotenuse 10
\n" ); document.write( "(d/2)^2 + ((d+4)/2)^2 = 10^2 (solve for d)
\n" ); document.write( "1/4 * d^2 + 1/4 * (d+4)^2 = 100
\n" ); document.write( "d^2 + (d+4)^2 = 400 (multiplied both sides by 4)
\n" ); document.write( "d^2 + d^2 + 8d + 16 = 400
\n" ); document.write( "2 * d^2 + 8d + 16 = 400
\n" ); document.write( "d^2 + 4d + 8 = 200 (divided both sides by 2)
\n" ); document.write( "d^2 + 4d - 192 = 0 (16*12=192)
\n" ); document.write( "(d + 16)(d - 12) = 0 (2 answers use the positive one)
\n" ); document.write( "d = 12 inches
\n" ); document.write( "so d+4 = 16 inches
\n" ); document.write( "now we got measure of both diagonals\r
\n" ); document.write( "\n" ); document.write( "Area = 1/2 times the product of the diagonals
\n" ); document.write( "Area = 1/2 * 12 * 16
\n" ); document.write( "Area = 1/2 * 192
\n" ); document.write( "Area = 96 inches^2\r
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