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The area of rhombus whose perimeter is 80m and one of the diagonal is 24m.
  • a)
    284m2
  • b)
    384m2
  • c)
    192m2
  • d)
    374m2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The area of rhombus whose perimeter is 80m and one of the diagonal is ...
Side of rhombus = 
∴ Length of other diagonal

∴ 
= 16 × 24 cm2 = 384 cm2
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Community Answer
The area of rhombus whose perimeter is 80m and one of the diagonal is ...
To find the area of a rhombus, we need to know the length of one of its diagonals. In this case, we are given the perimeter and one of the diagonals of the rhombus.

Given:
Perimeter of the rhombus = 80m
Length of one diagonal = 24m

Finding the side length of the rhombus:
Since the perimeter of the rhombus is the sum of all its sides, we can divide the perimeter by 4 to find the length of each side.
Perimeter = 4 * side length
80 = 4 * side length
Side length = 80 / 4
Side length = 20m

Finding the other diagonal of the rhombus:
The diagonals of a rhombus bisect each other at right angles. This means that the length of each diagonal can be found using the Pythagorean theorem.

Let's consider half of the diagonal as the base of a right-angled triangle, with one side being half the side length of the rhombus (10m) and the other side being the unknown length of the diagonal.
Using the Pythagorean theorem, we can find the length of the diagonal.

(diagonal/2)^2 = (side/2)^2 + (side/2)^2
(diagonal/2)^2 = 10^2 + 10^2
(diagonal/2)^2 = 200
diagonal/2 = √200
diagonal = 2 * √200
diagonal ≈ 2 * 14.14
diagonal ≈ 28.28m

Calculating the area of the rhombus:
The area of a rhombus can be calculated by multiplying the lengths of the diagonals and dividing by 2.
Area = (diagonal 1 * diagonal 2) / 2
Area = (24 * 28.28) / 2
Area ≈ 339.36 / 2
Area ≈ 169.68m²

Therefore, the correct answer is option B) 384m².
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