# Algebra

Sabrinia is building a rectangular raised flower bed. The boards on the two shorter sides are 6 inches thick, and the boards on the two longer sides are 4 inches thick. Sabrina wants the outer length of her bed to be 4 times its height and the outer width to be 2 times its height. She also wants the boards to rise 4 inches above the level of the soil in the bed. What should the outer dimesnions of the bed be if she wants it to hold 3136 cubic inches of soil?

1. 👍 1
2. 👎 0
3. 👁 867
1. If the boards are h inches high, then the soil is (h-4)" deep.

If the outside dimensions are x and y, with x<y,

x=2h
y=4h

So, the inner dimensions are (x-8) and (y-12), and using the given volume,

(h-4)(x-8)(y-12) = 3136
h(2h-8)(4h-12) = 3136
h = 11 inches.

Check:
The outer width is 22
The outer length is 44
The inner width is 14
The inner length is 32
The depth is 7

14*32*7 = 3136

Nice problem! At first I thought not enough information was provided.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### algebra

you are building a rock wall for a flower bed along your 38-foot long driveway. You Want the wall to be one-half of the length of the driveway with an absolute deviation of at most 3 feet. write and solve an absolute value

2. ### Calculus

a rectangular storage area is to be constructed along the sides of a tall building. A security fence is required along the three remaining sides of the area. What is the maximum area that can be enclosed with 1000m fencing?

3. ### Math

Mark is building a custom wooden frame around his flower bed.The length of the frame is 5.45 feet, and the width of the frame is3.275 feet. What is the area of the flower bed without rounding?_________square feet

4. ### differential calculus

a man 6 ft tall is walking toward a building at the rate of 4 ft/sec. if there is a light on the ground 40 ft from the building, how fast is the man's shadow on the building growing shorter when he is 30 ft from the building?

1. ### diff calculus

1.) triangular corner lot has perpendicular sides of lengths 120 feet and 160 feet. Find the dimensions of the largest rectangular building that can be constructed on the lot with sides parallel to the streets.

2. ### Gr10 math

A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower bed?

3. ### math

Russell planted a flower bed that is 1.6 square meters Jackie planted a flower bed that is 16 tenths square meters. Draw a quick picture to model the two areas

4. ### math

A flower bed has 26 rows of flowers and each row has 8 flowers. one section of the flower bed contains red flower . There are 8 rows of red flowers. the rest of the flower bed is white flowers . how many white flowers are there

1. ### Math

A flower bed is 4 meters wide and 5 meters long. What is the area of the flower bed in square feet? Round intermediate calculations and your answer to the nearest hundredth.

2. ### Math Calculus

Three sides of a fence and an existing wall form a rectangular enclosure. The total length of a fence used for the three sides is 240 ft. Let x be the length of two sides perpendicular to the wall as shown. Write an equation of

3. ### bussiness math

Angela Hatcher is planting flower bulbs in her garden for this coming summer. She intends to plant 1 bulb for every 5 square inches of flower bed. How many flower bulbs will she need for an area measuring 230 square inches?

4. ### Algebra

A rectangular region with one side against an existing building is to be fenced in. Assume that there is 150 ft of material available. Since one side is the building, you will use your material to construct 3 sides of the