Question

WILL GIVE BRAILIEST: 8th grade: equations and geometry

Answer 1

That’s should he right but also it could of been 54

Answer 2

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

$P= 2l+2w$ 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.:

$\left \{ {{20=2(j+4)+2h} \atop {30=2(3h)+2(j+1)}} \right.$

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.

$20=2(j+4)+2h$

Start by distributing 2 into j + 4.

$20=2j+8+2h$

Now subtract 8 from both sides of the equation.

$12=2j+2h$

Now isolate variable j by subtracting 2h from both sides of the equation.

$12-2h=2j$

Now condense the equation into simple terms by dividing both sides by its GCF 2 then reorder to get j on the left.

$j=6-h$

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.

$30=6h+2j+2$

Subtract two from both sides to isolate the variables

$28=6h+2j$

Now we can plug j into our equation

$28=6h+2(6-h)$

Step 4: Distribute 2 into 6-h

$28=6h+12-2h$

Step 5: Combine like terms

$28=4h+12$

Step 6: Subtract 12 from both sides of the equation

$16=4h$

Step 7: Divide both sides by 4

$4=h$

Now that we know that h=4 we can plug 4 into one of our earlier equations. I used j=6-h

$j=6-4\\j=2$

Plug answers into either one of the original equations to check answer