For what values of r will the area of the shaded region be greater than or equal to 12 square units? Write your answer as an inequality.

STEP 2: The values are .

Answer:

Draw a rectangle.. write 13 on the two longer sides of the rectangle then write 7 on the other two shorter ones. Then add them all up and there you go your answer!

Our equation would be 13 +  13 + 7 + 7 = 40 inches

Step-by-step explanation:

The values of r for which the shaded region will be greater than or equal to 12 square units is;

r ≥ 8

We can see a rectangle and a triangle in the given image.

With the triangle being the unshaded portion of the rectangle.

Thus;

Area of shaded portion = Area of rectangle - area of rectangle.

We know that formula for area of rectangle is;

A_r = length × width

Thus; A_r = 3 × r

A_r = 3r

Area of a triangle is;

A_t = ½ × base × height

A_t = ½ × r × 3

A_t = ½(3r)

Thus;

Area of shaded portion = 3r - ½(3r)

Area of unshaded portion = 1.5r

We are told that the area of the unshaded region should be greater than or equal to 12. Thus;

1.5r ≥ 12

r ≥ 12/1.5

r ≥ 8

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