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The longer diagonal of a rhombus is three times the length of the shorter diagonal is x, what expression gives the perimeter of the rhombus? The perimeter of the rhombus is__.

Respuesta :

Answer:

4(√2.5)x

Step-by-step explanation:

Let each side of the dragonal be P

Bringing out a Triangle out of the rhombus we have a right angle triangle with the base of x/2 and height of 3/2x.

And the hypothenus is P.

Applying Pythagoras theorem we have

p ^2= (1.5x)^2+(0.5X)^2

p ^2= 2.25X^2 +0.25X^2

P = (√2.5) X

Since the Rhombus consist of 4 triangles . The perimeter can best be expressed as 4 x the perimeter of the triangle.

P= 4(√2.5)x.

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