Question

a bookcase is to be constructed as shown in the figure below. the height of the bookcase is 2 feet longer than the length of a shelf. if 22 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.

Answer 1

The length of the shelf is 10 feet while its height is 10 feet.

Equation

Equation is an expression used to show the relationship between the sides and angles of a right angled triangle.

Let x represent the shelf length and y represent the shelf height.

The height of the bookcase is 2 feet longer than the length of a shelf. hence:

• y = x + 2
• -x + y = 2   (1)

Also, 22 feet of lumber is available:

• x + y = 22   (2)

From equation 1 and 2:

y = 12, x = 10

The length of the shelf is 10 feet while its height is 10 feet.

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