Question

A rectangular building has a length of L and a width of W. A scale model of the building is constructed that is 24 times as small as the original building. Which of the following expressions represent the perimeter of the scale model?

Select all that apply.

2(1/24L+1/24W)
1/24L+1/24W
48L+48W
1/24L+1/24W+1/24L+1/24W
2(24L+24W)
1/12L+1/12W

Answer 1

Options 1, 4, and 6 represent the perimeter of the scale model.

Step-by-step explanation:

Step 1:

The rectangular building has a length of L and a width of W.

The scale model is 24 times smaller than the original building so the length of the scaled building is
`(1)/(24)L` and the width is
`(1)/(24)W`.

Step 2:

The perimeter of any given rectangle is twice the sum of the length and the width of the same rectangle.

The perimeter
`=2(length+width).`

By substituting the values, we get

The perimeter
`= 2 ((1)/(24)L +(1)/(24) W )`, this is the first option.

Step 3:

By expanding this we get
`(2)/(24)L +(2)/(24) W= (1)/(12) L + (1)/(12) W`, which is the sixth option.

We can also expand it as follows;
`2 ((1)/(24)L +(1)/(24) W ) = (1)/(24)L +(1)/(24)L +(1)/(24) W+(1)/(24) W.`

This is the fourth option.

So options 1,4, and 6 represent the perimeter of the scaled model.