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Answer:
dimensions are 51x91
Step-by-step explanation:
Assuming that the gym is rectangular in shape, then...
l*w=4641
and 2l+2w=284
We have two variables and two equations so to solve this we plug one equation into another.
Solve for one variable:
l*w=4641
w=4641/l
Plug into the other equation...
2l+2(4641/l)=284
Solve
l*(2l+9282/l)=284
2l^2+9282=284l
2l^2-284l+9282=0
Factor the trinomial:
2(l−51)(l−91)=0
l−51=0 or l−91=0(Set factors equal to 0)
l=51 or l=91
now, lets plug it into one of the equations to find w
51*w=4641
w=91, l=51
or...
91*w=4641
w=51, l=91
Answer:
91 ft × 51 ft
Step-by-step explanation:
while the other answer is basically correct, it makes a to at the beginning of the calculation (but the continues correctly).
and it assumes you can find the right factoring of the expression.
so, I will show you here how to generally solve this, even if you cannot find the right factorization :
l×w = 4,641 ft²
w = 4641/l
2l + 2w = 284
2l + 2(4641/l) = 284
2l + 9282/l = 284
2l² + 9282 = 284l
2l² - 284l + 9282 = 0
to make things easier let's divide everything by 2
l² - 142l + 4641 = 0
the general solution to a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = l
a = 1
b = -142
c = 4641
l = (142 ± sqrt((-142)² - 4×1×4641))/(2×1) =
= (142 ± sqrt(20,164 - 18,564))/2 =
= (142 ± sqrt(1600))/2 = (142 ± 40)/2 = 71 ± 20
l1 = 71 + 20 = 91
l2 = 71 - 20 = 51
w1 = 4641/91 = 51
w2 = 4641/51 = 91
so, they are interchangeable (it does not matter which we call length and which width).
the dimensions are 91 ft × 51 ft