Area of the Rhombus whose perimeter is equal to 40 if one diagonal is

1.	Area of the Rhombus whose perimeter is equal to 40 if one diagonal is equal to 16
Answer» Answer: ar (rhombus) = 96 square units. Step-by-step explanation: ____________________________________ $\setlength{\unitlength}{1cm}\begin{picture}(6,6)\thicklines\put(0,0){\line(-1,-2){1.5}}\put(0,0){\line(1,0){4}}\put(4,0){\line(-1,-2){1.5}}\put(-1.5,-3){\line(1,0){4}}\put(-1,0){A}\put(4.3,0){B}\put(3,-3){C}\put(-2,-3){D}\qbezier(0,0)(1.7,-2)(2.45,-3)\qbezier(-1.5,-3)(1,-1.5)(4,0) \put(1.2,-1.2){O}\end{picture}$ ____________________________________ LET, Side of rhombus = S then, perimeter of rhombus = 40 4 S = 40 S = 10 units ____________________________________ Let, Diagonal AC = 16 units then, ∵ diagonals of rhombus bisect each other perpendicularly ∴ OA = 8 units ; ∠ AOD = 90° and , Side = AD = 10 units ____________________________________ Using Pythagoras theorem in Δ AOD OA² + OD² = AD² ( 8 )² + OD² = (10)² OD² = 100 - 64 OD² = 36 OD = 6 units ____________________________________ Now, BD = 2 (OD) = 2 (6) = 12 units so, we have Diagonals of rhombus as d₁ = 16 units and d₂ = 12 units therefore, ar (rhombus) = 1/2 × d₁ × d₂ ar (rhombus) = 1/2 × 16 × 12 ar (rhombus) = 96 square units. ____________________________________

Area of the Rhombus whose perimeter is equal to 40 if one diagonal is equal to 16

Answer»

Answer:

ar (rhombus) = 96 square units.

Step-by-step explanation:

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LET,

Side of rhombus = S

then,

perimeter of rhombus = 40

4 S = 40

S = 10 units

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Let,

Diagonal AC = 16 units

then,

∵ diagonals of rhombus bisect each other perpendicularly

∴ OA = 8 units ;

∠ AOD = 90°

and , Side = AD = 10 units

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Using Pythagoras theorem in Δ AOD

OA² + OD² = AD²

( 8 )² + OD² = (10)²

OD² = 100 - 64

OD² = 36

OD = 6 units

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Now,

BD = 2 (OD) = 2 (6) = 12 units

so,

we have Diagonals of rhombus as

d₁ = 16 units and d₂ = 12 units

therefore,

ar (rhombus) = 1/2 × d₁ × d₂

ar (rhombus) = 1/2 × 16 × 12

ar (rhombus) = 96 square units.

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