SOLUTION: the length of a rectangle is 4 times the width and the perimeter is 30. How can I show my son how I arrived At the answer

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Question 1126929: the length of a rectangle is 4 times the width and the perimeter is 30. How can I show my son how I arrived At the answer
Found 3 solutions by ikleyn, josmiceli, math_helper:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
Let W be the rectangle width.


Then its length is 4 times W, or 4W, according to the condition.


The perimeter is the sum of lengths of all 4 sides:


    Perimeter = L  + W + L  + W,   or

    Perimeter = 4W + W + 4W + W = 10W.


It is equal to  30, according to the condition.


So, you have an equation


    10W = 30.


To solve the equation, divide both sides by 10. You will get


    W = 30/10 = 3 units.


So, the width is 3 units.

Hence, the length is 4 times 3 units, or 4*3 = 12 units.


Answer.  The width is 3 units;  the length is 12 units.

Solved.   //   My congratulations to you and to your son ! 

    As the conclusion, ask your son to re-tell this solution to you.

    Be sure to say him "Good job !" when he will complete it !

    Ask him if he wants to get more solutions and explanations from me.

    If he (and you) want it, I will be happy to be in touch !

------------

1.   Please let me know whether you understand my solution and whether your son understand it.   Thank you.


2.   Notice that there is no question in your post,  which is  VERY BAD.

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Closely related to it are these lessons, that you can read too to upgrade your knowledge
    - Solved problems on the perimeter and side lengths of a triangle
    - Solved problems on the perimeter and side lengths of a right-angled triangle
    - Solved problems on the perimeter and the side lengths of a parallelogram
    - Solved problems on the perimeter and side lengths of a rectangle
(as well as your son's knowledge).


Good luck and happy learning to you and to your son !


Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the width
= the length





and

It is a 3 x 12 rectangle
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
L = length
W = width
(1) L = 4W (from "length is 4 times the width")
(2) 2L + 2W = 30 (from perimeter info)
Substitute for L (=4W) from eq 1 into eq 2. I'll go step-by-step:
2(4W) + 2W = 30
8W + 2W = 30
10W = 30
W = 30/10 = 3


W=3 implies L = 4*3 = 12 (using eq 1)


——
Answer: width is 3, length is 12
——

Check: 2L + 2W should be 30: 2(12) + 2(3) = 24 + 6 = 30 (ok)
(and L=4W is true b/c we used that fact to compute L from W, can always re-check: L=12=4*3 = 4W (ok))

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