Question

The square shown is dilated by a factor of 2. What is the area, in square units, of the dilated square?

Answer 1

18

Explanation:

To solve this problem, you could either do this two ways: solve for x immediately and then multiply it by 2, or you could multiply the equation by two and solve for x.

I will be using the first option.

Step 1: Solve for x

`-2x+7=-4x+11\\\\` - We can set these equal to each other because a square has all sides congruent, which means that this side and all the others are equal to each other

`-2x+2x+7=-4x+2x+11\\\\7=-2x+11`- We add 2x to both sides so we can isolate all the variables on one side and all the constants on one

`7-11=-2x+11-11\\\\-4=-2x`- We do this so all the constants are on one side

`(-4)/(-2)=(-2x)/(-2) \\\\2=x`- We divide by the coefficient of x so that we can fully isolate it

So now we have what x is, so we have to reinsert x into the equations and multiply it by itself to find the original area, after that we multiply it by 2.

`-2x+7\\\\-2(2)+7\\\\-4+7\\\\3*3=9\\\\9*2=18`