IXL | Perimeter and area: changes in scale

Look at this square:

9 in

If the side lengths are doubled, then which of the following statements about its perimeter will be true?

The ratio of the new perimeter to the old perimeter will be

1:2

The ratio of the new perimeter to the old perimeter will be

4:1

The ratio of the new perimeter to the old perimeter will be

2:1

The ratio of the new perimeter to the old perimeter will be

3:1

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Learn with an example

question

Look at this rectangle:

4 mm

3 mm

If both dimensions are tripled, then which of the following statements about its perimeter will be true?

The new perimeter will be

times the old perimeter.

The new perimeter will be

times the old perimeter.

The new perimeter will be

times the old perimeter.

The new perimeter will be

of the old perimeter.

solution

You can solve this problem without using the measurements given in the diagram.

The original rectangle had this perimeter:

P = 2(b + h)

The new rectangle will have 3 times the base and 3 times the height. Since the original dimensions were b and h, the new dimensions will be 3b and 3h. Calculate the perimeter:

P	=	2(3b + 3h)

	=	2 · 3(b + h)

	=	6(b + h)

Divide the new perimeter by the original perimeter and simplify.

new perimeter

original perimeter

6(b + h)

2(b + h)

The new perimeter will be

times the old perimeter.

Looking for more? Try these:

Lesson: Perimeter

Lesson: Area of rectangles

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Teacher tools

Work it out

Not feeling ready yet? These can help:

BB.1Perimeter

BB.2Area of rectangles and parallelograms

GG.6Area of triangles

L.1Understanding ratios

Lesson: Perimeter

Lesson: Area of rectangles

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