the area of a rhombus whose perimeter is 80 m and one of its diagonal is 24 m is?
plz plz answer this...it will be a great help for me
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the area of a rhombus whose perimeter is 80 m and one of its diagonal is 24 m is?
plz plz answer this...it will be a great help for me
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Verified answer
Given :
Aim :
Solution :
Properties of Rhombus :
Answer :
Perimeter of rhombus = side + side + side + side → 4 × side
→ 80m
Let the side be x.
→ x = 20m
Hence, side of the rhombus = 20m
By using the Pythagoras theorem let us find the other Diagonal.
☞ ½ × 24 = 12m
Area of ∆AOD :
(base)² + (height)² = (hypotenuse)²
Here,
Substituting the values,
➜ y² + 12² = 20²
➜ y² = 20² - 12²
Using identity a² - b² = (a + b)(a - b)
➜ y² = (20 - 12)(20 + 12)
➜ y² = (8)(32)
➜ y² = 256 m
Transposing the powers,
➜ y = √256
➜ y = 16m
½ of Diagonal 2 = 16m
Hence,
Diagonal 2 = 16 × 2 → 32m
Now that we have the values of both the diagonals,
Area of Rhombus :
Therefore, the Area of the Rhombus is 384m²
More Formulas :