# SOLUTION: The Diagonals of Rhombus measure 16cm and 30cm.Find its perimeter

Algebra ->  Algebra  -> Triangles -> SOLUTION: The Diagonals of Rhombus measure 16cm and 30cm.Find its perimeter      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Geometry: Triangles Solvers Lessons Answers archive Quiz In Depth

 Question 333740: The Diagonals of Rhombus measure 16cm and 30cm.Find its perimeterAnswer by Edwin McCravy(8908)   (Show Source): You can put this solution on YOUR website!``` Here is the rhombus drawn twice, once with each diagonal. The four sides of a rhombus have equal measures. Let each side have length x. Then the perimeter of the rhombus will be 4x. The drawings below are to scale: Looking at the lower triangular half of the left drawing we use the law of cosines on triangle ABC: Divide every term by 2 ------------------- Now we look at the left triangular half of the right drawing, and we use the law of cosines again, this time on triangle ABD: Divide every term by 2 --------- Here are the two equations we have found above: A rhombus is a parallelogram, and the adjacent angles in a parallelogram are supplementary. Therefore the sum of the measures of angles A and B is 180°. Therefore B = 180° - A Therefore we use the identity: , and get: cos(B) = cos(180°-A) = -cos(A) We substitute -cos(A) for cos(B) in the first equation and simplify: Now we put that together with the other equation and we have this system: When we add those two equations term-by term, the terms on the right cancel and we get: Divide both sides by 2 Taking positive square roots of both sides: So the perimeter is 4x or 4(17) or 68. Edwin```