SOLUTION: A school gym has a perimeter of 324 feet and an area of 6,480 square feet. What are the dimensions of the gym?
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Question 930286: A school gym has a perimeter of 324 feet and an area of 6,480 square feet. What are the dimensions of the gym?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
2L + 2w = 324
L = (324 - 2w)/2
Lw = 6480
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Lw = 6480
w(324 - 2w)/2 = 6480
324w - 2ww = 6480*2
2ww - 324w + 6480*2 = 0
ww - 162w + 6480 = 0
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the above quadratic equation is in standard form, with a=1, b=-162 and c=6480
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -162 6480
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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w = 90
w = 72
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either root will work for this problem:
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w = 72
L = (324 - 2w)/2
L = (324 - 2*72)/2
L = 90
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answer:
w = 72 ft
L = 90 ft
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