Question

the length of a rectangle is 3 feet less than twice the width of the rectangle. if the perimeter of the rectangle is 324 feet, find the width and the length?

Answer 1

To find the width and length of the rectangle, set up equations using the given information. The width of the rectangle is 55 feet and the length is 107 feet.

Step-by-step explanation:

To find the width and length of the rectangle, we can set up equations using the given information. Let's start with the equation for the perimeter of a rectangle: P = 2L + 2W. Given that the length (L) is 2 times the width (W) minus 3 feet, we can substitute the expressions for length and width into the perimeter equation. So we have:

324 = 2(2W - 3) + 2W.

Simplifying the equation, we get:

324 = 4W - 6 + 2W.

Combining like terms, we have:

324 = 6W - 6.

Adding 6 to both sides of the equation, we get:

330 = 6W.

Dividing both sides of the equation by 6, we get:

W = 55.

Therefore, the width of the rectangle is 55 feet. To find the length, we can substitute the value of W into the expression for length: L = 2W - 3. So we have:

L = 2(55) - 3.

Simplifying the expression, we get:

L = 107.

Therefore, the length of the rectangle is 107 feet.

Answer 2

Ok you should start by drawing a rectangle for the width you just label x and for the length it will be labeled 2x-3 because it's 3 ft less than twice the width now you need to know that you find perimeter by adding up all the sides so do that but I prefer multiplying each side by 2 because in a rectangle each side repeats twice so this is how I would solve it
2(x)+2(2x-3)=324
2x+4x-6=324. Distributing
6x-6=324. Adding like terms
+6. +6
6x=330. Now divide by 6
X=55
Now are width we labeled as just x so we plug that in and our width is 55 ft
Now we have to plug in 55 for our equation we made for the length
2(55)-3
110-3=107ft for your length