What is the scale factor of the triangles ABE & DBC ?

In other words, you'll use the SAS similarity property with 3/2 as the scale factor

Explanation:

Choice A is not correct because we don't have enough info about all three pairs of sides.

Instead we'll go with SAS similarity. This is the idea where we'll use two pairs of sides to see if they are in the same proportion, and we'll also use the included angle between the two sides. The angles ABE and DBC are congruent as they are vertical angles. So that's where the "A" comes from in "SAS".

As for the S terms, we divide the corresponding sides like so

DB/AB = 9/6 = 3/2

BC/BE = 1.5/1 = 15/10 = 3/2

The scale factor as a fraction is 3/2, which converts to the decimal form 1.5

This says that triangle DBC has sides that are 3/2 = 1.5 times longer than corresponding sides in triangle ABE.

If you're curious how the sides correspond, then look at the ordering of ABE and DBC. The order is important when it comes to similar triangles.

AB and DB are the first two letters of ABE and DBC respectively. So we have AB pair up with DB.

Similarly, BE and BC pair up because they are the last two letters of ABE and DBC respectively.

We divide sides of DBC over sides of ABE to get the scale factor from ABE to DBC. The scale factor must be some result larger than 1 do indicate an enlargement is going on.

2.56 is the width of the garden

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for