Question

Find the perimeter of rectangle EFGH , with vertices
E (−3,9 )
F ( 1,9 )
G ( 1,−5 )
H ( −3,−5 )
Whats the units??

Answer 1

To find the perimeter of rectangle EFGH, we need to find the distance between each pair of adjacent vertices and then sum them up.

First, let's find the distance between vertices E and F:
Distance EF = √[(1 - (-3))^2 + (9 - 9)^2]
Distance EF = √[4^2 + 0^2]
Distance EF = √16
Distance EF = 4 units

Next, let's find the distance between vertices F and G:
Distance FG = √[(1 - 1)^2 + (-5 - 9)^2]
Distance FG = √[0^2 + (-14)^2]
Distance FG = √196
Distance FG = 14 units

Then, let's find the distance between vertices G and H:
Distance GH = √[(-3 - 1)^2 + (-5 - (-5))^2]
Distance GH = √[(-4)^2 + 0^2]
Distance GH = √16
Distance GH = 4 units

Finally, let's find the distance between vertices H and E:
Distance HE = √[(-3 - (-3))^2 + (-5 - 9)^2]
Distance HE = √[0^2 + (-14)^2]
Distance HE = √196
Distance HE = 14 units

Now, we sum up all the distances to find the perimeter:
Perimeter = EF + FG + GH + HE
Perimeter = 4 + 14 + 4 + 14
Perimeter = 36 units

Therefore, the perimeter of rectangle EFGH is 36 units.