Question

What is the measure of x?​

Answer 1

x= 9 inches

Explanation:

Hello

I can help you with this.

in this case, we have two similar triangles, let's see

Step 1

identify the rigth triangles.

1) the first triangle has these dimensions

hypotenuse( remember, the longest side)= unknown=H

adjacent side(the horizontal)=6 +x

opposite side(the vertical)=10

2) the second triangle has these dimensions

hypotenuse( remember, the longest side)= unknown=h

adjacent side(the horizontal)=6

opposite side(the vertical)=4.

As these triangles keep the same proportion and in both cases we know the length of the legs, we can establish a relationship

Step 2

establish a relationship

let's compare the opposite side and the adjacent side

triangle 1 (the bigger)

`proportion= (opposite\ side)/(adjacent\ side)\\proportion= (10)/(6+x)`

Triangle 2

`proportion= (opposite\ side)/(adjacent\ side)\\proportion= (4)/(6)\\proportion=(2)/(3)`

were the proportions are equal, so

`(10)/(6+x)=(2)/(3)`

at this point, just isolate x to find its value

Step 3

isolate x

`(10)/(6+x)=(2)/(3)\\multiply\ both\ sides\ by\ 3\\(10*3)/(6+x)=(2*3)/(3)\\(30)/(6+x) =2\\\\Multiply\ both\ sides\ by (6+x)\\(30(6+X))/(6+x) =2(6+x)\\30=12+2x\\30-12=2x\\18=2x\\so\\x=(18)/(2) \\x=9`

remember the units of measure ( Inches)

x= 9 inches

I really hope it helps, have a nice day.