Math Question Width/Length

Question

The width of a rectangle is 11 inches more than the length. The perimeter is 258 inches. Find the length and width

Answer 1

Hello Blah,

I am going to provide a solution here with the understanding that in nearly all cases in Euclidean Geometry, the length is the longest.

So, first let's develop some expressions to represent the length and width. Then, we will use the formula for the perimeter because it will allow us to determine the real value in numerical distance versus algebraic form, okay?

According to the above problem, let:

The length equal x and

The width equal x + 11

Again, the length is considered the longer side of a rectangle so I do encourage you to check to see if you transcribed the problem correctly here, okay?

The formula for determining the perimeter of a rectangle is as follows:

P = 2(l + w) or P = 2(l) + 2(w) where P equals perimeter, l equals the length and w equals the width. You will notice that the second formula is simply the first one with the distributive property of math applied. It is the one I prefer using so we will go with that one, fair enough?

P = 2(l) + 2(w)

258 = 2(x) + 2(x + 11)

258 = 2x + 2x + 22

258 = 4x + 22

236 = 4x

x = 59 <-------This is the length according to the problem above.

To determine the width all we need do is substitute 59 for x in the expression we developed for width.

w = x + 11

w = 59 + 11

w = 70 <-------This is the width according to the problem above.

Finally, we should always check our work, right? To do so, let's use the formula for the perimeter and substitute the values we obtained for length and width to ensure they equal 258 inches,

P = 2(l) +2(w)

258 = 2(59) + 2(70)

258 = 118 + 140

258 = 258

The solution checks out meaning it is valid. Again, I want to remind you to check the problem to ensure what you transcribed here is correct due to one of the properties of a rectangle reflecting the width being longer than the length,

I hope I helped and wish you a great rest of the week. I hope you feel the liberty to leave any feedback about the solution, or seek further clarity to any portion of the solution. Best!