SOLUTION: the ratio of lenght to width of a rectangle corral is to be 8 to 5. enough lumber is available for a 78-yard fence the (perimeter). What will be the length and width of the corral

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Question 249126: the ratio of lenght to width of a rectangle corral is to be 8 to 5. enough lumber is available for a 78-yard fence the (perimeter). What will be the length and width of the corral if all the lumber is used? write two equations and in two unknowns and solve
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
ratio of length to width is 3/5
p = 78
2*L + 2*W = 78

L/W = 3/5
cross multiply to get 3W = 5L
divide both sides by 3 to get:
W = 5L/3

substitute for W in perimeter equation to get:
2*L + 2*(5*L/3) = 78
simplify by removing parentheses to get:
2*L + 10*L/3 = 78
multiply both sides of equation by 3 to get:
3*2*L + 10*L = 78*3
simplify to get:
6*L + 10*L = 234
combine like terms to get:
16*L = 234
divide both sides by 16 to get:
L = 234/16 = 14.625
W = 5*L/3 = 5*14.625/3 = 24.375

you have:
L = 14.625
W = 24.375

L/W = 3/5 = .6

L/W = 14.625/24.375 = 3/5 after you divide both numerator and denominator by 4.875

ratio is good.

perimeter is equal to:

2*L + 2*W which becomes:

2*14.625 + 2*24.375 = 29.25 + 48.75 = 78

perimeter is good.

your answer is:

length = 14.625 yards
width = 24.375 yards