Problems based on the properties of rhombus :- If the length of one side of a rhombus is 7.5 cm , find the lengths of the remaining sides. Ans: given :- Length of one side of rhombus = 7.5 cm Let us consider, (AB) = 7.5 cm l (AB) = (BC) = (CD) = (DA) l l l l ∴ (∵ sides of a rhombus are equal – properties of rhombus) (BC) = (CD) = (DA) = 7.5 cm l l l ∴ The diagonals seg XZ and seg YW of the rhombus XYZW intersect at a point P. If (XP) = 8 cm, find (XZ). l l Ans: given :- (XP) = 8 cm and l The diagonals seg XZ and seg YW of the rhombus XYZW intersect at a point P. i.e. (XP) = (PZ) = 8 cm l l by using properties of rhombus, diagonals of rhombus bisect each other. i.e. (XP) = (PZ) = l l = ∴ 8 cm (XZ) = 2 × 8 cm l ∴ (XZ) = 16 cm l ∴
Problems based on the properties of rhombus :- If the length of one side of a rhombus is 7.5 cm , find the lengths of the remaining sides. Ans: given :- Length of one side of rhombus = 7.5 cm Let us consider, l (AB) = 7.5 cm ∴ l (AB) = l (BC) = l (CD) = l (DA) (∵ sides of a rhombus are equal – properties of rhombus) ∴ l (BC) = l (CD) = l (DA) = 7.5 cm The diagonals seg XZ and seg YW of the rhombus XYZW intersect at a point P. If l (XP) = 8 cm, find l (XZ). Ans: given :- l (XP) = 8 cm and The diagonals seg XZ and seg YW of the rhombus XYZW intersect at a point P. i.e. l (XP) = l (PZ) = 8 cm by using properties of rhombus, diagonals of rhombus bisect each other. i.e. l (XP) = l (PZ) = ∴ 8 cm = ∴ l (XZ) = 2 × 8 cm ∴ l (XZ) = 16 cm