Let the length of the rectangle be L and the width be W. L= 2W+3--(1) 2L+2W=60--(2) Substituting for L in the equation (2), 2(2W+3)+2W= 60 4W+6+2W=60 6W=60-6 6W=54 W=9 Substituting in equation (1), L=(2x9)+3 L=18+3 L=21 The dimensions of the rectangle are: Length = 21 units. Width = 9 units.
I read the problem incorrectly as the length being 3 time the width. Yes the words went in but my mind processed it wrong. After I realized this mistake it was easy to solve in my head. This is why I was a computer type instead of an electrical engineer.
I did it with a mental picture. At first I had 2 short sides at 10 and 2 long sides at 20 = 60. I like working in tens if the answer is in tens. It usually gets me in the ball park.Then I bumped the short sides down to 9 and the long sides to 18 and then up on long sides by 3 to 21. Bingo. My battleship method worked first time.
So LENGTH = (WIDTH x 2) + 3 L = 2W + 3 and W + W + 2W + 3 + 2W + 3 = 60 Length x 2 + Width x 2 = Perimeter 6W + 6 = 60 6W = 54 W = 9 The Width is 9 and the length is 9 x 2 + 3 = 21
Let the length of the rectangle be L and the width be W.
L= 2W+3--(1)
2L+2W=60--(2)
Substituting for L in the equation (2),
2(2W+3)+2W= 60
4W+6+2W=60
6W=60-6
6W=54
W=9
Substituting in equation (1),
L=(2x9)+3
L=18+3
L=21
The dimensions of the rectangle are:
Length = 21 units.
Width = 9 units.
l = length
w = width
l = 2w + 3
2(l) + 2(w) = 60
2(2w + 3) + 2w = 60
4w + 6 + 2w = 60
6w + 6 = 60
-6 -6
6w = 54
w = 9
l = 21
I read the problem incorrectly as the length being
3 time the width. Yes the words went in but my
mind processed it wrong. After I realized this
mistake it was easy to solve in my head.
This is why I was a computer type instead of an
electrical engineer.
I can see the video title now: "I calculated the voltage wrong! You'll be SHOCKED by what happens next!!"
I did it with a mental picture. At first I had 2 short sides at 10 and 2 long sides at 20 = 60. I like working in tens if the answer is in tens. It usually gets me in the ball park.Then I bumped the short sides down to 9 and the long sides to 18 and then up on long sides by 3 to 21. Bingo. My battleship method worked first time.
L = 3 + 2W and L + W = 60/2 = 30
Now substitute (3 + 2W) + W = 30 or 3W = 27
So W = 9 and L = 3 + 2 . (9) = 3 + 18 = 21
1. 2L+2w=P=60 given: rectangle, 4 sides, opposite sides equal
2. thus L+w=1/2*P=60/2=30 smaller numbers are easier divide by 2
3. L=2w+3 given: Length in terms of width
4. thus 2w+3+w=3w+3=30 smaller numbers are easier divide by 3
5. therefore w+1=10
6. w=10-1=9 answer part 1✔
7. L+9=30
8. therefore L= 30-9=21 answer part 2✔
9. check P=2(L+w)=2(21+9)=2*30=60 answer correct✔
I agree with trevor bowling. Increase your acumen.
I love algebra and love solving equations. I got this correct. Keeps me sharp.
Length plus width = 30, so W is width and length is (2W +3). W + 2W + 3 = 30. 3W = 27. W =9 and L = 21.
structure:
two equations in two unknowns
UNKNOWNS
L: length
W: width
EQUATIONS:
eq.1 60 = 2L+2W
eq.2 L = 3+2W
subtract eq.2 from eq 1
60-L = 2L+2W -(3 +2W)
60-L = 2L-3
63=3L
L = 21 sol.1
eq.2 L = 3+2W
21 = 3+2W
18 = 2W
W = 9 sol.2
EQUATIONS:
eq.1 60 = 2L+2W
60=?2(21)+2(9)
60=?42+18
60=❤60✔️
eq.2 L = 3+2W
21=?3+2(9)
21=?3+18
21=❤21✔️
FINAL ANSWER
L = 21 sol.1
W = 9 sol.2
Easy Took off 6 for the extra length then divided 54 by 6 to get9
Width 9
Length 2*9+3=21
Did it in my head.
W = 9
L = 21
9 and 21
So LENGTH = (WIDTH x 2) + 3 L = 2W + 3
and W + W + 2W + 3 + 2W + 3 = 60 Length x 2 + Width x 2 = Perimeter
6W + 6 = 60 6W = 54 W = 9
The Width is 9 and the length is 9 x 2 + 3 = 21
I set my equation up a bit differently.
Where _x_ is width, and _2x+3_ is the length:
2(x+2x+3)=60
2x+4x+6=60
-6 -6
6x=54
x=9
2x+3=21
W=9
L=21
60/2 = 30
30 - 3 = 27
27 = 2*W+W
27 = 2*9+9
27-2*9 = 9 = (W)
27-9 = 2*9 = 18
18+3 = 21 = (L)
L = 21
W = 9
9x21
3w + 3 = 30
3w = 27
w = 9
l = 2w + 3
l = 21
L=21, W=9
L=21
W=9
got 9, 21 X and 2X + 3 so 6X + 6 = 60 simple equation thanks for the fun
let width = x and length = 3 + 2x = 2x + 3
l = 2x + 3
--------------------------------
| |
| | w = x
| |
--------------------------------
perimeter rectangle = 2l + 2w ---> p = 2(2x +3) + 2x = 60
p = 4x + 6 + 2x = 60 4x + 2x + 6 = 60 6x + 6 = 60
make x the subject ---> 6x + 6 - 6 = 60 - 6 6x = 54
6x = 54 6x/6 = 54/6 x = 9
dimension width ---> w = x = 9
dimension length ---> l = 2(9) +3 = 21
proof :: perimeter of a rectangle ---> p = 2l + 2w = 2(21) + 2(9) = 42 + 18 = 60
(w,l)=(9,21) in about eight seconds in my head. Too long. I know. Sorry, I'm really beat.
I did it the same way. Pretty easy wasn't it!
Calculator?? I solved it without a pencil!
Wrong And is 36x 24
W=9 , l=21
9 and 21