Vince has a rectangular rug in his room with an area of 10 ft the length of the rug is 18 inches longer than the width what could be the dimensions of the rug?

The length of the rug is 4 ft.

The width of the rug is 2.5 ft.

Explanation:

The area of the rug is 10 ft.

The length of the rug be l.

Let us convert the inches to feet.

Thus,

Thus, the length of the rug is

Let the width of the rug be w.

Substituting these values in the formula of area of the rectangle, we get,

Solving the expression using the quadratic formula,

Substituting the values, we have,

Thus,

 and  

Since, the value of w cannot be negative, the value of w is 2.5ft

Thus, the width of the rug is 2.5ft

Substituting in , we get,

Thus, the length of the rug is 4 ft.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is