What is the perimeter of a rhombus? 1)Its area is 140 sq

Question

What is the perimeter of a rhombus?
1)Its area is 140 sq meters
2) One of its diagonals is 48 meters

plz show your work

ywilfred · Answer

What is the perimeter of a rhombus? 
1)Its area is 140 sq meters 
2) One of its diagonals is 48 meters 

1) sides of rhombus are all equal, so x^2 = 140
 So sufficient
 
2) One of the diagonals is 48
 using pythagoras' theorem, you can work out that
 sqrt(x^2+x^2) = 48
 2x^2 = 2304
 So sufficient
 
Both equations are sufficient to solve the problem. So D should be the asnwer

marine777 · Answer

Is rhombus(although its sides are equal) a square, if not then x^2 = 140 is invalid 
Area of rhombus with diag d1 and d2 : 1/2d1d2 and
sides & diag relation is : 4x^2 = d1^2+d2^2 

Rhombus: A parallelogram with four equal sides; an oblique-angled equilateral parallelogram

ywilfred · Answer

I believe a rhmobus has all the properties of a square. Let me go check it out, I can't remember it quite clearly. I'll post again once I've looked up my notebook.

ywilfred · Answer

Okay, this is what I got from my old maths notebook.

A rhmobus is a parallelogram with   4 equal sides  

A square is a parallelogam with   4 equal angles   and   4 equal side  s

The diagonals of a rhmobus are perpendicular to each other.
The diagonals of a rhmobus bisect the angles they join.

So a rhombus does have one property of a square, that is, all 4 sides are equal (so each side is x, so to speak)

mallelac · Answer

I think it is C.

The length of a side of rhombus is to be determined to calculate perimeter and the perimeter = 4*side

But, the diagonals bisect at 90degrees. It means that side^2 = (d1/2)^2 + (d2/2)^2 (Pythogorous theorem)

(1)Area is 140 sq. mt. 0.5*d1*d2 = 140. So, d1*d2 is known. It does not help us to find out the perimeter as the side cannot be determined. Insufficient.

(2)d1 = 48 meters. No idea about d2. So, insufficient again.

Combining (1) and (2), d1*d2 = 140 and d1 = 48. So, d2 is also known.

It means that from side^2 = (d1/2)^2 + (d2/2)^2, side can be determined. Thus, perimeter can also be determined. Thus, C is the answer.

Could you let me know OA (with explanation if I am wrong).

OlegC · Answer

clearly neither statement by itself is sufficient

rhombus area = (diagonal1 * diagonal2)/2
knowing diagonal1 and the area we can find the diagonal2
knowng the two diagonals we can use Pythagorean Theorem to find the lengths of the sides

Answer C

What is the perimeter of a rhombus? 1)Its area is 140 sq

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