find the length of the longer diagonal of a rhombus if the shorter diagonal is 12 and the perimeter is 36
+128597 The diagonals form right angles......so we have
[(1/2) the shorter diagonal]^2 + [(1/2) the longest diagonal]^2 = [(1/4) perimeter]^2
6^2 + d^2 = 9^2 where d is 1/2 the length of the longer diagonal......so.....by the Pythagorean Theorem, we have
√[9^2 - 6^2] = √[81 - 36 ] = √45 = 3√5 = d ...... and twice this = 6√5 = about 13.416
+128597 The diagonals form right angles......so we have
[(1/2) the shorter diagonal]^2 + [(1/2) the longest diagonal]^2 = [(1/4) perimeter]^2
6^2 + d^2 = 9^2 where d is 1/2 the length of the longer diagonal......so.....by the Pythagorean Theorem, we have
√[9^2 - 6^2] = √[81 - 36 ] = √45 = 3√5 = d ...... and twice this = 6√5 = about 13.416
