SOLUTION: How do I calculate The width of a rectangle is 10 feet less than half of its length. If all four sides of the rectangle add up to 52 feet, find the length and the width of this rec

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Question 669198: How do I calculate The width of a rectangle is 10 feet less than half of its length. If all four sides of the rectangle add up to 52 feet, find the length and the width of this rectangle.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let L equal the length
let W equal the width
the width is 10 feet less than half the length.
W = L/2 - 10
P = perimeter
P = 2W + 2L
P = 52
2W + 2L = 52
substitute L/2 - 10 for W in this equation to get:
2 * (L/2 - 10) + 2L = 52
simplify to get:
L - 20 + 2L = 52
combine like terms to get:
3L - 20 = 52
add 20 to both sides to get:
3L = 72
divide both sides by 3 to get:
L = 24

you have L = 24
you have W = L/2 - 10 which gets you W = 24/2 - 10 which becomes W = 2

you have L = 24 and W = 2
2L + 2W = 52 which becomes 48 + 4 = 52 so the perimeter is good.
W = L/2 - 10 becomes W = 24/2 - 10 which becomes W = 12 - 10 which becomes W = 2 which is also good.

the measurements checkout so the solution is good.
L = 24
W = 2