In rhombus ABCD, AC = 40 cm and BD = 42 cm. Find the perimeter of Ap
Answers
Perimeter of Rhombus ABCD = 116 cm if AC = 40 cm and BD = 42 cm
Step-by-step explanation:
In rhombus ABCD, AC = 40 cm and BD = 42 cm
Diagonal of a rhombus bisect perpendiculary each other
Let say they bisect at O
AO = OC = AC/2 = 40/2 = 20 cm
BO = OD = BD/2 = 42/2 = 21 cm
ΔAOB ≅ ΔBOC ≅ ΔCOD ≅ Δ DOA
AB² = AO² + BO²
=> AB² = 20² + 21²
=> AB² = 400 + 441
=> AB² = 841
=> AB² = 29²
=> AB = 29
All sides of rhombus are equal
AB = BC = CD = AD = 29 cm
Perimeter of Rhombus ABCD = 29 + 29 + 29 + 29 = 116
Perimeter of Rhombus ABCD = 116 cm
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Step-by-step explanation:
In rhombus ABCD, AC = 40 cm and BD = 42 cm
Diagonal of a rhombus bisect perpendiculary each other
Let say they bisect at O
AO = OC = AC/2 = 40/2 = 20 cm
BO = OD = BD/2 = 42/2 = 21 cm
ΔAOB ≅ ΔBOC ≅ ΔCOD ≅ Δ DOA
AB² = AO² + BO²
=> AB² = 20² + 21²
=> AB² = 400 + 441
=> AB² = 841
=> AB² = 29²
=> AB = 29
All sides of rhombus are equal
AB = BC = CD = AD = 29 cm
Perimeter of Rhombus ABCD = 29 + 29 + 29 + 29 = 116
Perimeter of Rhombus ABCD = 116 cm