Question 817049: Studying quadratic equations. Can you help with an equation for this word problem?
Laura wants to plant a rectangular garden next to her house. she needs to enclose the garden with a fence, and will use the house as one side of the fence. If laura has 63 feet of fencing to use, what is the maximum area that she can enclose? What are the dimensions of the garden?
Found 2 solutions by TimothyLamb, josgarithmetic:
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! 63 = 2w + L
L = 63 - 2w
a = wL
---
a = wL
a = w(63 - 2w)
a = 63w - 2w^2
---
a(w) = -2w^2 + 63w
---
the above quadratic equation is in standard form, with a=-2, b=63, and c=0
---
to solve the quadratic equation, plug this:
-2 63 0
into this: https://sooeet.com/math/quadratic-equation-solver.php
---
the quadratic vertex is a maximum at ( w= 15.75, a(w)= 496.125 )
---
Answer:
the maximum area is 496.125 sq.ft ( a(w) from the vertex )
w = 15.75 ft ( w from the vertex )
L = 31.50 ft ( calculated from above equation for L using w )
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Convert fractions, decimals, and percents:
https://sooeet.com/math/fraction-decimal-percent.php
---
Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php
Answer by josgarithmetic(39617)  (Show Source):
|
|
|
