Inequalities for Geometric Problems Practice 1. A sandbox in the shape of a rectangular prism is 1/2ft. high and needs to contain at least 42 ft.³ of sand. How would you write an inequality to express the possible area of the base, b, of the sandbox? 2. Gus is knitting a scarf in the shape of a parallelogram. The height of the parallelogram will be 25 cm. He only has enough yarn to knit a maximum area of 1,000 cm². How would you write an inequality to express the possible length of the base, b, of the parallelogram? 3. A playing area for children is being laid out in the shape of a rectangle. It will be 8 feet wide and must contain more than 100 ft.². How would you write an inequality to express the possible base length, b, of the playing area? 4. The area of a parallelogram must be less than 180 cm². The base is 15 cm. How would you write and solve an inequality describing h, the height of the parallelogram? 5. A box of sugar needs to contain more than 60 in.³. The height of the box is 8 inches. How would you write and solve an inequality describing b, the area of the base of the box?
1. Let b be the length of the base of the sandbox.
Volume of rectangular prism = base area x height
Therefore, b x 1/2 = 42
b = 84
So, the inequality would be b > 84
2. Let b be the length of the base of the parallelogram.
Area of parallelogram = base x height
Therefore, b x 25 < 1000
b < 40
So, the inequality would be b < 40
3. Let b be the length of the base of the playing area.
Area of rectangle = length x width
Therefore, b x 8 > 100
b > 12.5
So, the inequality would be b > 12.5
4. Let h be the height of the parallelogram.
Area of parallelogram = base x height
Therefore, 15 x h < 180
h < 12
So, the inequality would be h < 12
5. Let b be the area of the base of the box.
Volume of box = base area x height
Therefore, b x 8 > 60
b > 7.5
So, the inequality would be b > 7.5