Find the perimeter of rectangle efgh with vertices E(6,9) and F(4,9), G(4,-5),H(6,-5)

1 answer

To find the perimeter of a rectangle, we need to add up the lengths of all four sides.

Given the coordinates of the vertices E(6,9), F(4,9), G(4,-5), and H(6,-5), we can find the lengths of the sides by using the distance formula: d = √((x2-x1)^2 + (y2-y1)^2).

The distance between E and F (side EF) is:
√((4-6)^2 + (9-9)^2) = √((-2)^2 + 0^2) = √(4) = 2.

The distance between F and G (side FG) is:
√((4-4)^2 + (9-(-5))^2) = √(0^2 + 14^2) = √(196) = 14.

The distance between G and H (side GH) is:
√((6-4)^2 + (-5-(-5))^2) = √(2^2 + 0^2) = √(4) = 2.

The distance between H and E (side HE) is:
√((6-6)^2 + (-5-9)^2) = √(0^2 + (-14)^2) = √(196) = 14.

Now, we can add up the lengths of all four sides to find the perimeter:
2 + 14 + 2 + 14 = 32.

Therefore, the perimeter of rectangle EFHG is 32 units.