Question

the perimeter of a rhombus is 260 cm and the height is 10 cm . if one diagnol is 0.25 m, find the length of other diagnol also in metres.

Answer 1

All four sides of a rhombus have equal measures, so each side is of the perimeter or = 65. So we label the upper left side 65. We are given that one of the diagonals is 66. Let that be the red diagonal below. Since the diagonals bisect each other the top half of the red diagonal is of 66 or 33. So we label the top half of the red diagonal 33. We want to know the length of the green diagonal. So we label the left half of the green diagonal x. Since the diagonals of a rhombus are perpendicular, the triangle with the sides x,33, and 65 is a right triangle, so we can use the Pythagorean theorem to find x: x² + 33² = 65² x² + 1089 = 4225 x² = 3136 x = √3136 x = 56 So half the green diagonal is 56 cm. Therefore, the whole green diagonal is 2×56 = 112 cm