The vertices of a quadrilateral in the coordinate plane are known. how can the perimeter of the figure be found? use the distance formula to find the length of each side, and then add the lengths. use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel. use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicular. use the distance formula to find the length of the sides, and then multiply two of the side lengths.

"Use the distance formula to find the length of each side, and then add the lengths".

Step-by-step explanation:

By definition the perimeter of a quadrilateral is the sum of the length of its sides.

Therefore the first thing we should find is the length of the sides of the quadrilateral

If we have the vertices A, B, C and D of the quadrilateral then the distance between two of its vertices is the length of one of its sides.

For example, the distance between vertex A and vertex B is the length of the AB side. Then, using the formula of the distance between two points, we find the length of its sides and add them together.

Then the correct answer is: "Use the distance formula to find the length of each side, and then add the lengths".

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

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