1, find the lengths of the side a rhombus whose diagonals are 6cm and 8cm.
2, if a diagonal of a square is 12 cm long then how long is each side a square.
1. The diagonals of a rhombus are perpendicular bisectors of each other, meaning they divide the rhombus into four right-angled triangles. Since the diagonals are 6cm and 8cm, the sides of the rhombus can be found using the Pythagorean Theorem in one of the right-angled triangles:
a^2 + b^2 = c^2
a^2 + (3cm)^2 = (4cm)^2
a^2 + 9cm^2 = 16cm^2
a^2 = 16cm^2 - 9cm^2
a^2 = 7cm^2
a = √7 cm
Therefore, each side of the rhombus is approximately 2.65cm.
2. Since a diagonal of a square divides the square into two congruent right-angled triangles, we can again use the Pythagorean Theorem to find the length of each side of the square:
a^2 + a^2 = (12cm)^2
2a^2 = 144cm^2
a^2 = 72cm^2
a = √72 cm
Therefore, each side of the square is approximately 8.49cm.