A bookcase is to be constructed as shown in the figure below. The height of the bookcase is 4 feet longer than the length of a shelf. If 20 feet of lumber is available for the entire unit (including the shelves, but NOT the back of the bookcase), find the length and height of the unit

h = l + 4

Assume a box, but the two shelves will not necessarily be at the top and bottom of the box. Find the perimeter.

2h + 2l = 20

Substitute l + 4 for h in the second equation and solve for l. Put that value in the first equation to find h. Check by putting both values into the second equation.

find the ratio of whole numbers that is equivaletion to the radio of 16 ft to 10 yd.

To find the length and height of the bookcase unit, we need to set up an equation based on the given information.

Let's assume the length of each shelf is "x" feet.

According to the information given, the height of the bookcase is 4 feet longer than the length of a shelf, so the height is (x + 4) feet.

Now, let's consider the lumber used for the shelves. Since there are four shelves, each shelf will use 2x feet of lumber (two sides of each shelf). Therefore, the total lumber used for the shelves is 4 * 2x = 8x feet.

We also need to account for the lumber used for the vertical sides of the bookcase, which contribute to both the length and height. Each side has a length of x feet and a height of (x + 4) feet. So, each side uses 2 * ((x + 4) + x) = 4 * (x + 2) feet of lumber.

Considering the lumber used for both shelves and sides, the total lumber used for the entire unit is 8x + 4 * (x + 2) = 8x + 4x + 8 = 12x + 8 feet.

The total available lumber is given as 20 feet. Therefore, we can set up an equation:

12x + 8 = 20

To solve for x, we subtract 8 from both sides of the equation:

12x = 12

Finally, we divide both sides by 12:

x = 1

So, the length of each shelf is 1 foot.

To find the length and height of the unit, we substitute x = 1 into the equations:

Length = x = 1 foot
Height = x + 4 = 1 + 4 = 5 feet

Therefore, the length of the unit is 1 foot and the height is 5 feet.

To find the length and height of the bookcase, we need to set up and solve a system of equations based on the given information.

Let's use "x" to represent the length of each shelf.

From the problem statement, we know that the height of the bookcase is 4 feet longer than the length of a shelf. So, the height can be represented as "x + 4".

We also know that the total length of lumber available for the entire unit is 20 feet. Since each shelf is x feet long, and there are two shelves in the bookcase (one on top of the other), the total length of the shelves can be represented as "2x".

Therefore, our first equation is:
2x = 20

To find the length of each shelf, we can solve this equation:
2x = 20
Divide both sides of the equation by 2:
x = 10

So, the length of each shelf is 10 feet.

Now, we can substitute this value back into our equation for the height of the bookcase:
Height = x + 4 = 10 + 4 = 14 feet

Therefore, the length of the unit (each shelf) is 10 feet, and the height of the unit is 14 feet.