Question

Can someone solve this?

Answer 1

Answer:

B : $4x\sqrt{17}$

Step-by-step explanation:

If you divide a rhombus using its diagonals, you get 4 right triangles, whose legs are both 1/2 the length of the diagonals.

This means that the legs of one of those 4 triangles have lengths of 2x/2, and 8x/2, so the legs of one of those triangles x and 4x. This makes the length of one side equal to $\sqrt{x^{2} + (4x)^{2}} = \sqrt{17x^2} = x\sqrt{17}$. Because all 4 sides are the same length, you multiply this value by 4, and get $4x\sqrt{17}$, which is B.