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One interior angle of a rhombus is 150. The area of the rhombus is 50 square meters. What is the perimeter of the rhombus in meters?

 Feb 27, 2021
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A rhombus has two pairs of angles, and all 4 added together is 360, or one of each pair together is 180. This means that the other angle of the rhombus is 30. we also know that the area of the rhombus is diagonal1*diagonal2/2, or if we slant it so that one of the edges is like a base, we can do the height*base without dividing by 2. We'll use the second option, because if we draw a line from a corner orthogonal/perpendicular to the base, we have a 30,60,90 triangle. we know that the hypotenuse or the edge of the rhombus is 2 times the height of the triangle, so we can say that x^2/2=50, where x is the length of the edge, so simplifying, we get x=10, so the perimeter of the rhombus is 4x=$\boxed{40}$

 Feb 27, 2021

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