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the perimeter of a rhombus is 100 cm. One one of its diagonals is 40cm. Find the length of other diagonal .​

Answer 1

$P=2\times\sqrt{(1st\:diagonal)^2+(2nd\:diagonal)^2} \\\\100=2\times \sqrt{40^2+(2nd\:diagonal)^2} \\\\50=\sqrt{40^2+(2nd\:diagonal)^2} \\\\(2nd\:diagonal)^2=50^2-40^2\\\\(2nd\:diagonal)^2=2500-1600\\\\(2nd\:diagonal)^2=900\\\\2nd\:diagonal=\sqrt{900} \\\\2nd\:diagonal=30\:cm$