In the figure below, triangle abc is similar to triangle pqr, as shown below:
what is the length of side pq?
a) 18
b) 4
c) 32
d) 6

So, Option A is correct.

Step-by-step explanation:

If the triangles are similar, then the sides are proportional

If triangle ABC is similar to triangle PQR

then sides

AB/PQ = BC/QR = AC/PR

We need to find PQ

We are given AB = 6, BC =8 and QR=24

AB/PQ = BC/QR

Putting values:

6/PQ = 8/24

Cross multiplying:

6*24 = 8*PQ

144/8 = PQ

=> PQ = 18

So, Option A is correct.

Option A

Step-by-step explanation:

Two triangles are similar if the length of their sides is proportional.

In this case we have the triangle ∆ABC and ∆PQR so for the sides of the triangles they are proportional it must be fulfilled that:

In this case we know that:

Therefore

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.