Question
If the area of A rhombus is 240 sq. meter and perimeter is 68 meter, find out the lengths of the diagonals?
Answers
Steve
each side is 17, so its height is 17sinθ
where θ is the acute angle between its sides.
Thus,
17 * 17sinθ = 240
sinθ = 240/289
Now you have θ, and the diagonals are found using the law of cosines:
d^2 = 17^2 + 17^2 ± 2*17^2 cosθ
= 2*17^2 (1±cosθ)
where θ is the acute angle between its sides.
Thus,
17 * 17sinθ = 240
sinθ = 240/289
Now you have θ, and the diagonals are found using the law of cosines:
d^2 = 17^2 + 17^2 ± 2*17^2 cosθ
= 2*17^2 (1±cosθ)