Basic Geometry assist » plane Geometry » quadrilateral » Rectangles » how to find if rectangles are comparable

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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 

*
centimeters and also 100 centimeters; the other has dimensions 400 centimeters and 
*
centimeters.

What value of 

*
makes this a true statement?


Explanation:

For polygons to be similar, side lengths need to be in proportion.

Case 1:

*
 and 100 in the an initial rectangle exchange mail to 
*
and 400 in the second, respectively.

The resulting proportion would be:

*

*

*

*

This is difficult since 

*
need to be a hopeful side length.

Case 2:

*
 and 100 in the very first rectangle correspond to 400 and 
*
in the second, respectively.

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

*
 and the various other an area of
*
. If the an initial has a base size of
*
, what is the height of the second rectangle?


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.

*

*
 

*
 is the ratio factor that will be used to resolve for the elevation of the 2nd rectangle. This may be substituted right into the area formula for the 2nd rectangle. 

*

*

*

*

*

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

*
 and the 2nd one has a perimeter of
*
. The very first rectangle has a height of
*
. If the two rectangles room similiar, what is the basic of the 2nd rectangle?


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. 

*

*

*

*
 is the ratio variable we will usage to resolve for the base of the 2nd rectangle. 

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

*
and also a broad of
*
, providing us with the following ratio:

*

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:

*
This proportion compares the ratio in between the long sides in every rectangle to the ratio of the brief sides in every rectangle. If they are the same, cross-multiplying will produce a true statement, and also the rectangles are similar:

*

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: 

*
cross-multiply

*
because that"s true, the rectangles are similar.

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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