Answer:
#1: x=8, #2: x=21, #3: x=9
Step-by-step explanation:
So, to solve each of these x's, we need to do two things:
Find the scale factor
Then scale for x.
So lets start off with the first one.
We have a side value fo 3.
In the scaled version, we have the same side with a value of 6.
To find the scale, divide the 6 by 3:
6/3
=
2
So our scale is 2.
Next, lets look at our value on the traingle we know, and solve for the unkown x. We know that on the orginal traingle, its 4. For the version thats 2 times bigger, its x
So to solve this, multiply the 4 by 2:
4*2
=
8
This is your x value for the first question.
Next we have the side value 12 for the trapezoid. For the one next to it, the trapezoid has the same side with a value of 18.
To find the scale, lets divide 18 by 12.
18/12
=
1.5
That is our scale factor.
In these trapezoids, the bottom value is orginally 14.
In the scaled version, which we know is 1.5 times bigger, we have x.
To solve for x, lets multiply the 14 by 1,5:
14*1.5
=
21
So we know our x is 21 for the second answer.
Finally we have the third question.
This one is opposite to the last ones, where the smaller value has the missing x value.
Here our top side value is 20.
On the scaled version it is 15.
Lets divide 15 by 20, instead of what we normally do. Which would have been 20 by 15:
15/20
=
.75
Now, with this scale factor, our x will be smaller than the known value. Looking at the side length, the orginal value is 12.
On the scaled side length that is 0.75 times as big, its x
So lets multiply 12 by 0.75:
12*0.75
=
9
So this is your last x value, for your third answer!
This might seem long and tedious, but its actually a simple way of thinking about it, and you may find that you can quickly do this in your head, instead of a shorter, more complex way.
Hope this helps!
