diagonals PR and QS of a rhombus PQRS are 20cm and 48cm respectively then find the side of rhombus and its perimeter.
Answers
Step-by-step explanation:
The above Photo is the solution for the given question.
Answer:
The side of rhombus is 26 cm.
The perimeter of the rhombus is 104 cm.
Step-by-step-explanation:
NOTE: Kindly refer to the attachment for the diagram.
In figure, ☐ PQRS is a rhombus.
∴ PQ = QR = RS = PS - - ( 1 ) [ Sides of a rhombus ]
Diagonals PR and QS intersect in point O.
PR = 20 cm
QS = 48 cm - - [ Given ]
Now, diagonals of a rhombus bisect each other.
PO = OR = ½ PR
⇒ PO = ½ × 20
⇒ PO = 10 cm
Also,
QO = OS = ½ QS
⇒ OS = ½ × 48
⇒ OS = 24 cm
Now, diagonals of a rhombus are perpendicular bisectors of each other.
∴ In ΔPOS, ∠POS = 90°
∴ ( PS )² = ( PO )² + ( OS )² - - [ Pythagoras theorem ]
⇒ ( PS )² = ( 10 )² + ( 24 )²
⇒ ( PS )² = 100 + 576
⇒ ( PS )² = 676
∴ PS = 26 cm - - [ Taking square roots ]
∴ PQ = QR = RS = PS = 26 cm [ From ( 1 ) ]
Now, we know that,
Perimeter of rhombus = 4 × side
∴ P ( ☐ PQRS ) = 4 × PS
⇒ P ( ☐ PQRS ) = 4 × 26
∴ P ( ☐ PQRS ) = 104 cm
Additional Information:
1. Rhombus:
A quadrilateral with all its four sides of equal measures is called as rhombus.
2. Properties of Rhombus:
1. All sides are congruent.
2. Opposite angles are congruent.
3. Diagonals bisect each other.
4. Diagonals are perpendicular bisectors of each other.
