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Note: figure not attracted to scale.

You are watching: The widths of two similar rectangles are 10 and 8

Examine the over figure.

What is

?

Two rectangles are similar. One rectangle has actually dimensions

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

What worth of

makes this a true statement?

Explanation:

For polygons to be similar, next lengths must be in proportion.

Case 1:

and 100 in the very first rectangle exchange mail to
and 400 in the second, respectively.

The resulting proportion would be:

This is difficult since

must be a hopeful side length.

Case 2:

and 100 in the very first rectangle exchange mail to 400 and
in the second, respectively.

The correct proportion statement should be:

Cross main point to resolve for

:

200 centimeter is the only possible solution.

Explanation:

All sides being same is a problem for congruency, no similarity. Similarity focuses on the ratio in between rectangles and not ~ above the equivalency of all sides. As for the statement regarding the equal angles, every rectangles nevertheless of similarity or congruency have four 90 degree angles.

Explanation:

For two rectangles to be similar, their sides need to be proportional (form equal ratios). The ratio of the two much longer sides have to equal the proportion of the two much shorter sides.

However, the left proportion in our proportion reduces.

We can then deal with by cross multiplying.

We then deal with by dividing.

Explanation:

For 2 rectangles to it is in similar, their sides must be in the exact same ratio.

This problem can be solved using ratios and cross multiplication.

Let"s represent the unknown width of the best rectangle as x.

Two rectangles room similar. One has actually an area of

and the other an area the
. If the an initial has a base length of
, what is the elevation of the second rectangle?

Explanation:

The score is to fix for the elevation of the second rectangle.

Similar rectangles function on proportionality - the is, the ratios that the sides between two rectangles will be the same. In bespeak to identify the height, we will be making use of this ide of ratios through solving for variables from the area.

First, it"s helpful to attain full dimensions for the first rectangle.

It is given that its base length is 5, and it has actually an area the 20.

This way the very first rectangle has actually the dimensions 5x4.

Now, we may utilize the ide of ratios for similarity. The side lengths the the very first rectangle is 5x4, so the 2nd recatangle must have actually sides that room proportional to the first"s.

We have the information for the first rectangle, for this reason the data may be substituted in.

is the ratio element that will be offered to settle for the height of the 2nd rectangle. This might be substituted right into the area formula because that the second rectangle.

Therefore, the elevation of the second rectangle is 10.

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### Example inquiry #7 : just how To find If Rectangles Are similar

There space two rectangles. One has actually a perimeter of

and the 2nd one has a perimeter of
. The an initial rectangle has actually a height of
. If the 2 rectangles are similiar, what is the basic of the second rectangle?

Explanation:

The score of this problem is to figure out what base length of the 2nd rectangle will make it similar to the very first rectangle.

Similar rectangles function on proportionality - the is, the ratios the the sides in between two rectangles will be the same. In stimulate to determine the base, we will certainly be using this principle of ratios through solving for variables from the perimeter.

First, every the size of the first rectangle must be calculated.

This have the right to be accomplished through using the perimeter equation:

This method the size of the first rectangle room 10x5. We will use this info for the ratios to calculation dimensions that would certainly yield the second rectangle similar because of proprotions.

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

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

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### Example inquiry #8 : just how To find If Rectangles Are comparable

The attached image represents the size of two different brands of made linoleum tile. If the 2 tiles are similar, what would be the length of the large tile, provided the info in the figure below?

Explanation:

Two rectangles are comparable if their length and width form the exact same ratio. The little tile has actually a width of

and also a width of
, offering us through the adhering to ratio:

Since the length of similar triangles is twice their respective width, the length of the huge tile have the right to be determined as such:

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### Example question #9 : just how To find If Rectangles Are comparable

Are this rectangles similar?

yes - scale aspect

no

yes - scale variable

yes - scale variable 2

no

Explanation:

To determine if these rectangles are similar, collection up a proportion:

This proportion compare the ratio in between the lengthy sides in each rectangle come the proportion of the brief sides in each rectangle. If they are the same, cross-multiplying will produce a true statement, and the rectangles space similar:

These rectangles aren"t similar.

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### Example concern #10 : just how To uncover If Rectangles Are similar

Are these rectangles similar?

yes - scale element 3

no

yes - scale aspect 2.5

yes - scale element

yes - scale factor 2.5

Explanation:

To determine if the rectangles space similar, set up a proportion compare the quick sides and also the long sides from every rectangle:

cross-multiply

because that"s true, the rectangles space similar.

To uncover the range factor, either division 25 through 10 or 7.5 by 3. Either means you will get 2.5.

See more: Determine The Name For Aqueous Hbr (Hydrobromic Acid), How To Write The Name For Hbr (Hydrobromic Acid)

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