Question

Please help! Please show all work! Thx!

Answer 1

Part A)

`86=2(x+22)`

Part B)

`l=26\text{ cm}`

Explanation:

We know that the rectangle has a length of (x+5) and a width of 12 cm.

Part A)

Remember the formula for the perimeter of a rectangle:

`P=2(l+w)`

We know that the perimeter is 86. Substitute that for P:

`86=2(l+w)`

Substitute (x+5) for the length l and 17 for w. So:

`86=2((x+5)+17)`

We can simplify this to acquire our equation:

`86=2(x+22)`

Part B)

To find the length, let's find our x first. We have the equation:

`86=2(x+22)`

Divide both sides by 2:

`43=x+22`

Now, subtract 22 from both sides. Therefore, our x is:

`x=21`

To find the length, remember that the length is:

`l=x+5`

Since we now know the value of x, substitute 21 for x:

`l=21+5`

Add:

`l=26\text{ cm}`

So, the length is 26 centimeters.

And we're done!