The length of a rectangle is 3 cm longer than its width. If the perimeter of the rectangle is 66 cm , find its length and width.

Answer 1

In this problem the perimeter is the sum of the ides of the rectangle which is P= 2x +2y

x= width y =length

y= x+3 is the length

1) Let use the perimeter to substitute P= 2x + 2y. 66 = 2x + 2(x+3)

2) let find the value of "x" . 66 = 2x + 2x +6 66 = 4x +6. subtracting 6 in both sides we get:

66-6=4x+6 -6

60 =4x. dividing both sides by 4. 60/4 =4 x/4. x=15 Width y= x+3. y=15+3= 18 Length

Therefore the width = 15 cms. and the Length =18 cms.

Note: To check your answer , remember that P = 2x +2y. or 66 = 2(15) +2(18). 66= 30 +36. 66=66.

if you have additional questions, I am here to help you reach for your goal!!

Answer 2

Perimeter is the length around all sides so P = L+L+L+L

Let x be the width and x+3 be the length.

x + x + x+3 + x+ 3 = 66

Combining the like terms, we now have 4x + 6 = 66

Subtract 6 from both sides: 4x + 60

Divide both sides by 4: x = 15 which is the length of the width.

The length is 3 cm longer so 15 + 3 = 18cm

Answer 3

In accordance with Wyzant's academic honesty policy, I won't be answering the question as presented above, but I will show you how to solve a problems of this exactly this form, with slightly different numbers. You should hopefully be able to follow along with my steps, and then apply them to the numbers you gave.

1. The first step in solving problems like this is to take the english given to us and translate it into math
2. "The length of the rectangle is 5 cm longer than its width" -> "L = W + 5"
3. "The perimeter of the rectangle is 90 cm" -> "90 = 2*L + 2*W"
4. Now we have two equations, one relates the two side lengths to the known perimeter value, and the other relates the length to the width. We can then use our new 'formula' for L in place of the L in our second equation:
5. 90 = 2*(W+5) + 2*W
6. Next we should collect all our W's so that we can solve for them, we will start by expanding the equation, then collect all the W's and then move all numbers to the otherside to solve for W.
7. 90 = 2*W + 10 + 2*W
8. 90 = 4*W + 10
9. 80 = 4*W
10. 20 = W
11. Now we know how long our rectangles width is (20 cm), and we can use our earlier "L= W + 5" equation to solve for the length:
12. L = 20 + 5
13. L = 25
14. Now, to write our final answers with correct units
15. Length = 25 cm
16. Width = 20 cm