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Question 1001916: The length of a rectangle is 5 inches less than 4 times the width. The perimeter is 100 inches. Find the length and the width.
The length is
inches and the width is
inches.
I would just like to know how to write this equation out and then I can take it from there just need an exaMPLE, pLEASE
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! perimeter = 2 * length + 2 * width
100 = 2 * length + 2 * width
the length of the rectangle is 5 inches (or centimeters0 less than 4 times the width.
you get length = 4 * width - 5
4 * width has to be greater than 5, otherwise length will be negative or 0.
when width = 6, length = 4*6-5 = 24-5 = 19
when width = 10, length = 4*10-5 = 40-5 = 35
etc.
now that you have solved for the length in terms of the width, you can replace length in the equation with 4 * width - 5 to get:
100 = 2 * (4 * width - 5) + 2 * width
simplify that to get:
100 = 8 * width - 10 + 2 * width.
combine like terms to get:
100 = 10 * width - 10
you can solve for width and, once you know that, you can solve for length.
you can use variable names to represent the length and the width.
when you do that, you will get something like the following.
perimeter = 2 * length + 2 * width
let x = length and y = width.
equation becomes perimeter = 2x + 2y
since perimeter = 100, equation becomes:
100 = 2x + 2y
you are given the length is 5 less than 4 times the width.
you get x = 4y - 5
in the equation of 100 = 2x + 2y, replace x with 4y - 5 to get:
100 = 2 * (4y-5) + 2y = 8y - 10 + 2y = 10y - 10
your equation is 100 = 10y - 10
y is the width
after you solve for y you can then use that value of y to solve for x.
same answer except now you are using x and y instead of length and width.
they both represent the same thing.
if you do this correctly, your answer should be:
length = 39
width = 11
length is 5 less than 4 times width when width = 11 becomes length = 5 less than 44 which becomes length = 39
100 = 2 * length + 2 * width becomes:
100 = 2*39 + 2*11 which becomes:
100 = 78 + 22 which becomes:
100 = 100
this confirms the solution is correct.
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