Triangles Widths & Lengths

Question

The length of a rectangle is 3 inches less than 2 times the width. The perimeter is 24 inches. Find the length and the width?

Answer 1

Good Morning, Kevin,

First, let's assign some expressions to represent the length and width of the rectangle, fair enough? I always recommend students draw a rectangle so they can see the expressions they are formulating to ensure it makes sense, okay?

Therefore:

Let x equal the width

Let 2x - 3 equals the length

Second, the formula or equation for determining the perimeter of a rectangle - which we need to use in order to solve this problem - is as follows:

P = 2( L + W) or P = 2(L) + 2(W) where P equals perimeter, L equals length, and W equals the width. Please notice, Kevin: the second equation is exactly the same as the first with the exception of applying the distributive property of mathematics, fair enough?

Third, let's substitute the information we are given in the problem in our equation. Therefore:

P = 2(L) + 2(W) <----------Notice we used the second equation.

24 = 2(2x -3) + 2(x) <----------This is the equation while substituting the values given

24 = 4x - 6 + 2x <----------We merely used the distributive property with each term

24 = 6x - 6 <----------We combined like terms

30 = 6x <-----------After combining like terms we are left with this.

x = 5 <-----------We divided each side by 6 and this is the width.

Fourth, let's substitute the 5 for x in the expression for length, okay?

(2*5 - 3)

(10 - 3) =

7 <------------This is our length.

Fifth and finally, let's check our work, okay? We can use the original equation and substitute 5 for W and 7 for L.

P = 2(L) + 2(W)

24 = 2(7) + 2(5)

24 = 14 + 10

24 = 24

The solution checks and out and therefore the answer is valid. I surely hope this assists and that you have a great weekend. Should you have additional questions, wish to leave feedback, or seek further clarity on any part of the solution I have provided you, please just click the "Add Comment" button and leave the information directly beneath this solution. Should you need one-on-one tutoring, please feel free to reach out to me or any tutor. Best!