Question

A certain rectangle has a perimeter of 22 units and an area of 30 square units. two of the vertices have coordinates at (2,2) and (2,7). find the two missing coordinates. use the coordinate plane to support your answer

Answer 1

2* (width + length) = 22 which can be restated

A) 2w + 2L = 22

Dividing "A" by 2 we get
A) w + L = 11
B) width * length = 30
length = 30 / width and we put this into equation "A"
 w + 30/width = 11
Multiplying both sides by width
width^2 + 30 = 11w

w^2 -11w + 30 =0
width = 5 and/or width =6
Therefore length = 5 and/or length =6
(2,2) (2,7)
Difference in x = 0 and difference in y = 5
So, we'll make x=6 and the 2 other coordinates are
(8, 2) and (8, 7)