Question

Dora wants to put up a vegetable garden in their backyard. If the perimeter of the garden is 32 m and the area is 60 m2, what must be the length and the width of the vegetable garden?​

Answer 1

Length=6
Width=10
Or vice versa

Answer 2

Step-by-step explanation:

so, it is an ideal rectangular shape ? because that is what the problem description is "hiding".

if that assumption is true, then we have

l = length

w = width

perimeter = 32 = 2×l + 2×w

=> 16 = l + w

l = 16 - w

area = 60 = l×w

now we use the perimeter equation to substitute in the area equation

60 = (16 - w) × w = 16w - w²

so, we get the squared equation

-w² + 16w - 60 = 0

the solution for such an equation is

x (or w in our case) = (-b ± sqrt(b² - 4ac))/(2a)

a = -1

b = 16

c = -60

w = (-16 ± sqrt(256 - 4×-1×-60))/-2 =

= (-16 ± sqrt(256 - 240))/-2 =

= (-16 ± sqrt(16))/-2 = (-16 ± 4)/-2

w1 = (-16 + 4) / -2 = -12/-2 = 6 m

w2 = (-16 - 4) / -2 = -20/-2 = 10 m

l1 = 16 - 6 = 10 m

l2 = 16 - 10 = 6 m

so, one of length and width must be 6 meter and the other 10 meter long. it does not matter which, as a rectangle turned by 90 degrees is still the same rectangle.