Calculate the Perimeter: Similar Rectangles with Base 14 Units

Q: What does it mean for rectangles to be similar?

Similar rectangles have the same shape but different sizes. This means all corresponding sides have the same ratio (called the scale factor).

Q: Why can't I just multiply the base by something to get the perimeter?

The perimeter includes both length and width. You need to find the scale factor first, then multiply the entire smaller perimeter by that factor.

Q: Do I need to find the unknown side X first?

No! Since the rectangles are similar, you can use the perimeter ratio directly. The ratio of perimeters equals the ratio of corresponding sides.

Similar Rectangle Ratios with Proportional Perimeters

Look at the two similar rectangles below and calculate the perimeter of the larger rectangle.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find the perimeter of the large rectangle.

00:09 Remember, opposite sides in a rectangle are equal.

00:16 So, the perimeter is the sum of all the sides.

00:22 Now, this is the perimeter of the small rectangle.

00:26 Let's label the rectangles as one and two.

00:29 The rectangles are similar. That's given to us.

00:34 The similarity ratio is the same as the ratio of their perimeters.

00:40 We will substitute the right values and find the perimeter.

00:48 Next, we'll isolate the perimeter, represented by P.

01:10 And that's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the two similar rectangles below and calculate the perimeter of the larger rectangle.

Step-by-step solution

Let's remember that in a rectangle there are two pairs of parallel and equal sides.

We will call the small triangle 1 and the large triangle 2.

We calculate the perimeter of the small triangle:

$P_1=2\times3.5+2\times1.5=10$ Since we know that the rectangles are similar:

$\frac{3.5}{14}=\frac{p_1}{p_2}$

We place the data we know for the perimeter:

$\frac{3.5}{14}=\frac{10}{p_2}$

$\frac{3.5}{14}\times p_{_2}=10$

$p_2=10\times\frac{14}{3.5}$

$P_2=40$

Final Answer

40 cm

Key Points to Remember

Essential concepts to master this topic

Similar Rectangles: All corresponding sides have the same ratio
Scale Factor: Divide corresponding sides: $\frac{14}{3.5} = 4$
Check: Verify perimeter ratio equals side ratio: $\frac{40}{10} = 4$ ✓

Common Mistakes

Avoid these frequent errors

Using addition instead of multiplication for scale factor
Don't add the difference between sides (14 - 3.5 = 10.5) to find the larger perimeter = wrong answer! This doesn't maintain proportional relationships. Always multiply the smaller perimeter by the scale factor to find the larger perimeter.

Practice Quiz

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Is rectangle ABCD similar to rectangle EFGH?

FAQ

Everything you need to know about this question

What does it mean for rectangles to be similar?

Similar rectangles have the same shape but different sizes. This means all corresponding sides have the same ratio (called the scale factor).

How do I find the scale factor?

Divide any side of the larger rectangle by the corresponding side of the smaller rectangle: $\frac{14}{3.5} = 4$ . The scale factor is 4.

Why can't I just multiply the base by something to get the perimeter?

The perimeter includes both length and width. You need to find the scale factor first, then multiply the entire smaller perimeter by that factor.

Do I need to find the unknown side X first?

No! Since the rectangles are similar, you can use the perimeter ratio directly. The ratio of perimeters equals the ratio of corresponding sides.

How can I check my answer is correct?

Calculate both perimeters and verify their ratio equals the side ratio: $\frac{40}{10} = \frac{14}{3.5} = 4$ ✓

What if the scale factor is a fraction?

If the larger rectangle were actually smaller, you'd get a fraction less than 1. The method stays the same - just multiply the known perimeter by your scale factor!

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