Question

How to slove this problem?

Answer 1

Since the kites are similar, their sides correspond.  You can set up proportions like this:

$\frac{40}{48} = \frac{20}{x}$

This states that 40 (small kite) is to 48 (big kite) as 20 (small kite) is to x (big kite).  After that, use cross-multiplication to solve for x:

$40x = 48*20 \\ 40x=960 \\ x=24$

x must be 24 units long.

Answer 2

So, since the polygons are similar, they will share a scale factor. 

The dilation is a reduction.

SF= preimage/image

SF=48/40

SF= 1.2

To find the value of x, multiply 20 by 1.2, so:

20(1.2)=24

Thus, x = 24

Now, to check if the sides are proportional (this will determine if the polygons are, in fact, similar.)

24/20=1.2
48/40=1.2

BTW, the missing side measure for the image is 40 since 48 is its corresponding side, and 48/1.2 (SF) is 40.

Hence, we have 48/40= 1.2

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