
Note: figure not drawn to scale.
You are watching: Can two different sized rectangles have the same area
Examine the over figure.

What is




Two rectangles room similar. One rectangle has actually dimensions


What value of

Explanation:
For polygons to be similar, side lengths need to be in proportion.
Case 1:


The resulting proportion would be:




This is difficult since

Case 2:


The correct proportion statement must be:

Cross multiply to deal with for




200 cm is the only possible solution.
Explanation:
All political parties being equal is a problem for congruency, not similarity. Similarity concentrates on the ratio in between rectangles and also not ~ above the equivalency of all sides. As for the statement regarding the same angles, every rectangles regardless of similarity or congruency have 4 90 degree angles.
Explanation:
For 2 rectangles to be similar, their sides need to be proportional (form equal ratios). The proportion of the two longer sides must equal the proportion of the two much shorter sides.

However, the left proportion in our proportion reduces.

We deserve to then resolve by overcome multiplying.


We then fix by dividing.

Explanation:
For two rectangles to it is in similar, their sides should be in the very same ratio.
This trouble can be addressed using ratios and also cross multiplication.

Let"s denote the unknown broad of the best rectangle together x.






Two rectangles space similar. One has an area of



Explanation:
The score is to deal with for the elevation of the second rectangle.
Similar rectangles function on proportionality - the is, the ratios the the sides in between two rectangles will be the same. In bespeak to recognize the height, we will be making use of this ide of ratios through fixing for variables indigenous the area.
First, it"s advantageous to accomplish full dimensions for the first rectangle.
It is given that its base size is 5, and also it has actually an area that 20.



This way the very first rectangle has actually the dimensions 5x4.
Now, we may utilize the ide of ratios because that similarity. The next lengths of the an initial rectangle is 5x4, for this reason the 2nd recatangle must have actually sides that are proportional come the first"s.

We have actually the info for the very first rectangle, so the data may be substituted in.








Therefore, the height of the second rectangle is 10.
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Example inquiry #7 : exactly how To find If Rectangles Are similar
There space two rectangles. One has a perimeter of



Possible Answers:
Correct answer:

Explanation:
The score of this problem is to figure out what base length of the 2nd rectangle will make it similar to the an initial rectangle.
Similar rectangles function top top proportionality - that is, the ratios that the sides in between two rectangles will be the same. In order to recognize the base, we will be making use of this concept of ratios through resolving for variables native the perimeter.
First, all the dimensions of the an initial rectangle should be calculated.
This deserve to be accomplished through making use of the perimeter equation:





This means the size of the an initial rectangle are 10x5. We will use this info for the ratios to calculate dimensions that would certainly yield the 2nd rectangle comparable because that proprotions.




This will need revisiting the perimeter equation because that the 2nd rectangle.






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Example inquiry #8 : how To uncover If Rectangles Are comparable
The attached photo represents the dimensions of two different brands of made linoleum tile. If the 2 tiles room similar, what would certainly be the length of the large tile, offered the details in the figure below?

Possible Answers:
Correct answer:

Explanation:
Two rectangles are similar if your length and also width kind the very same ratio. The tiny tile has actually a broad of



Since the size of similar triangles is double their corresponding width, the length of the big tile can be identified as such:

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Example inquiry #1 : exactly how To find If Rectangles Are similar
Are this rectangles similar?

Possible Answers:
yes - scale variable

yes - scale factor 2
yes - scale factor

no
Correct answer:
no
Explanation:
To determine if this rectangles are similar, set up a proportion:


These rectangles aren"t similar.
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Example inquiry #2 : just how To discover If Rectangles Are similar
Are this rectangles similar?

Possible Answers:
no
yes - scale element

yes - scale element 3
yes - scale factor 2.5
Correct answer:
yes - scale aspect 2.5
Explanation:
To determine if the rectangles are similar, collection up a proportion compare the short sides and the long sides from each rectangle:


To uncover the scale factor, either divide 25 by 10 or 7.5 by 3. Either method you will get 2.5.
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