Answer:
C. j=2 and h=4
Step-by-step explanation:
Step 1: Create a system of equations for your problem based off what we know.
- we should know that the equation to find the perimeter of something is
[tex]P= 2l+2w[/tex] where P is the perimeter, l is the length, and w is the width.
- we know that the perimeter of Rectangle P is 20 inches and that the perimeter of Rectangle Q is 30
- we know the length and width of both rectangles
Using this information, lets set up our system.:
[tex]\left \{ {{20=2(j+4)+2h} \atop {30=2(3h)+2(j+1)}} \right.[/tex]
Step 2: Using the top equation we're going to try to solve for one of the variables. I chose to solve for variable j.
[tex]20=2(j+4)+2h[/tex]
Start by distributing 2 into j + 4.
[tex]20=2j+8+2h[/tex]
Now subtract 8 from both sides of the equation.
[tex]12=2j+2h[/tex]
Now isolate variable j by subtracting 2h from both sides of the equation.
[tex]12-2h=2j[/tex]
Now condense the equation into simple terms by dividing both sides by its GCF 2 then reorder to get j on the left.
[tex]j=6-h[/tex]
Step 3: Now that we solved for variable j we can now substitute j into one of our equations from the original system. I chose to use the bottom equation and chose to distribute it before substituting.
[tex]30=6h+2j+2[/tex]
Subtract two from both sides to isolate the variables
[tex]28=6h+2j[/tex]
Now we can plug j into our equation
[tex]28=6h+2(6-h)[/tex]
Step 4: Distribute 2 into 6-h
[tex]28=6h+12-2h[/tex]
Step 5: Combine like terms
[tex]28=4h+12[/tex]
Step 6: Subtract 12 from both sides of the equation
[tex]16=4h[/tex]
Step 7: Divide both sides by 4
[tex]4=h[/tex]
Now that we know that h=4 we can plug 4 into one of our earlier equations. I used j=6-h
[tex]j=6-4\\j=2[/tex]
Plug answers into either one of the original equations to check answer
