Similar rectangles are defined as a property of being similar or equal. The symbol used for similar is ||. Similar rectangles are described as the rectangles that are exact same shape but are dissimilar sizes. Two similar rectangles if the lengths of their corresponding sides form a proportion. A proportion means the fraction of value a and b. That is, a proportion is expressing in the way of a/b.


Examples of Similar Rectangles:

Similar rectangles example 1:


Find the missing length of following similar rectangles:

gh1


Solution:

We can calculate the missing length of the given similar rectangles by using the similarity concepts.

Let z be the missing length of the given similar rectangles.


Now we can compare the side values of the given rectangles.

 From the figures, `(4)/(8)` =`z/12`

Here we are using the cross multiplication. Then we get

 4*12=8*z

48=8z

Divide by the value of 8 on both sides.

`48/8` =  `(8z)/(8)`                                                             

After simplifying we get,                                                               

6= z

After rearranging, we get the final answer.

z=6


Answer: 6


Similar rectangles example 2:


The following two rectangles are similar. Find the missing length.


gh2


Solution:

We can find missing length by using the values in the figure.

Let x be the missing length of the given triangle.                                          

From the similar rectangle figures, `12/15` =`x/10`

Here we are using the cross multiplication. Then we get

 12*10=15*x

120=15x

Divide by the value of 15 on both sides.

`120/15` = `(15x)/(15)`                                                            

After simplifying,

8= x

After rearranging, we get the final answer.

x=8


Answer: 8

Similar rectangles example 3:

Find the missing length of following figure:


gh3


Solution:

Let‘s’ be the missing length of similar rectangles.

From the figure,

`3/6` = `s/8`

Here we are using the cross multiplication. Then we get

3*8=6s

24=6s

s=`24/6`

s=4

Answer: 4


Practice Problems of Similar Rectangles:

  1. Find the missing length of the following figure:  Answer: 5

im1

2.  Find the missing length of following figure: Answer: 4

im2