(2) Algebra problem: Can you help?

*to get to the answer

What methods have you tried?

Since the formula for the perimeter is 2w + 2l = p, try this:
2(3x+1) + 2(x+5) = p

I realise now what I did wrong; I squared the numbers rather than simply multiplying them by 2.

Thank you for your help @PhiNotPi :)

One thing that can help when doing problems of this kind (trying to keep clear on the formulas for perimeter / circumference vs. area vs. volume can be difficult for students with their first exposure to these things) is to be sure to operate on the units as well as the numbers.

For example, if you imagine that the rectangle is 3X + 1 inches wide and X + 5 inches high, and you multiply those W inches * H inches, then you’ll get “W*H square inches” in the answer, which will tip you off that you just calculated Area, when what you wanted was a Length measure (just plain “inches”, not “square inches”).

Even professional engineers have to remember to do this.

I’d add that if you want to show the square of a number on a text-based site like this, the typographic convention is to write ^ (shift-6) to indicate exponentiation. Thus x^2 = “x-squared”. In some computer languages it’s written x**2.

Perimeter = the sum of all the side lengths
You have a rectangle with two sides being 3x+1, and the other two sides are x+5
so,
Perimeter = 2(3x+1) + 2(x+5)
Perimeter =6x +2 + 2x+ 10 (using FOIL)
Perimeter =8x +12

@adr I agree with your math but “FOIL” normally describes how you multiply two binomials – doesn’t really apply here & hate to confuse the OP even further.