# (2) Algebra problem: Can you help?

Afternoon.

I need help on an algebra question. The question is as follows:

‘Write an expression for the perimeter of this rectangle. Then simplify your answer.

When you multiply out the brackets, you will have:’

The answers are:

1. 8x + 12

2. 3×2 + 6x + 5

3. 3×2 + 5x + 6

4. 4x + 6

The rectangle has 2 sides labelled. One is 3x+1, the other is x+5

Can anyone please help me with how to get the answer? I have tried 3 different methods and have not come up with an answer in the list given.

Thank you.

Observing members:
0
Composing members:
0
## 7 Answers

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.

## Answer this question

This question is in the General Section. Responses must be helpful and on-topic.