Question

a student builds an model of her bedroom. the scale is 1:25 in the scale model, the students bed is 3 inches long how long is her actual bed ?

Answer 1

The size of actual bed is 75 inches

Explanation:

Scale refers to the ratio of the original dimension to the dimension on paper (miniaturised dimension). Since it is a ratio, it has no dimension.

Scale= original dimension/miniaturised dimension

Given that scale is 1:25

It means that every 1 inch on paper would correspond to 25 inches in reality.

The length of the model bed= 3 inches

Hence, the length of the original bed is 25*3 = 75 inches

∴ Length of the actual bed of the student is 75 inches.

Answer 2

By definition of scale, the length of the actual bed of the student is 75 inches.

In first place, you have to know that the scale is the relationship that exists between the magnitudes of a drawing and the actual dimensions.

That is, the scale is defined by two numbers that determine the relationship between the drawing and reality.

The first number of the proportion or relationship refers to the drawing on paper, while the second number of the proportion refers to the reality of the object (actual dimensions). This is, Scale = Drawing: Reality or $scale=\frac{drawing}{scale}$

The scales can be:

• Reduction scale: used when the size of the object is larger than the size of the sheet of paper.
• Magnification scale: used to represent small objects.
• Natural scale: it is used to represent objects with a drawing the same size as reality.

In this case, you know that:

• Scale= 1:25
• Drawing= 3 inches
• Reality= ?

Replacing in the definition of scale:

1:25= 3 inches: reality

or

$\frac{1}{25} =\frac{3 inches}{reality}$

Solving:

reality= 3 inches× 25

reality= 75 inches

In summary, the length of the actual bed of the student is 75 inches.

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