Can somebody help me with this math question?

Question

Classify the figure created by the solution region of the system of inequalities:

 

y≥ 1

y≤ 5

x≥ 0

x≤4 

 

 

A) parallelogram

B) rectangle

C)SQUARE
D)triangle

Answer 1

You can classify this figure by graphing the inequalities and seeing what shape they make.

 

y ≥ 1 is everything above the horizontal line at y = 1.

y ≤ 5 is everything below the horizontal line at y = 5.

x ≥ 0 is everything right of the vertical line at x = 0.

x ≤ 4 is everything left of the vertical line at x = 4.

 

Once you graph these inequalities, you can see that you have a four-sided shape (so it's not a triangle). Its sides meet at right angles since horizontal and vertical lines are always perpendicular. And its sides are all 4 units long (from 1 to 5 and from 0 to 4).

 

A four-sided shape with right-angled vertices and all sides congruent is a square (C). However, since all squares are also parallelograms and rectangles, it is also a parallelogram and a rectangle.