The area of a rectangle is twice the area of a square. If the rectangle is 6 inches long, and the width of the rectangle is the same as the length of a side of the square, find the dimensions of both the rectangle and the square.

Dimension of rectangle = 6 inches by 3 inches

Dimension of square = 3 inches by 3 inches

Step-by-step explanation:

Given information:

- Length of rectangle = inches.

- Width of rectangle is the same as the side length of square.

- Area of rectangle is twice the area of square

Variable to define:

Let = side length of the square and the width of the rectangle

Finding dimensions of rectangle and square:

From the information given, we can write the equation:

 (Area of rectangle is twice the area of square)

(Divide on both sides)

inches

Dimension of rectangle = length by width

= 6 inches by 3 inches

Dimension of square = side by side

= 3 inches by 3 inches

Hope this helps :)

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be