Can you help me find the dimensions of the garden?

Question

The length of a rectangular garden is 6 feet less than the width. Its area is 55 square feet. Find the dimensions of the garden.

Answer 1

Rectangle
Area= 55
L= W-6
W= x ( unknown) <<<<<< Given information Ingredients

Area = L*W <<<<<< Formula Recipe


Is this solvable? Yes, we have our ingredients for our recipe, because we know the relationship between the numbers. Area of a rectangle is found by multiplying length times width. We can use one unknown variable, x, because length is 6 less than width. Area of 55 is given.

Unknowns create an imbalance, so we solve for x by starting with nothing, trying to find balance.
The value for W is unknown, it is our target, so we label it x in the equation.

0= Area-Area
0=( x-6) * x - 55
0= x²-6x-55        we factor the workable ingredient, 55
                          factors of 55 are 1, 5, 11, 55
                           we factor x²-6x-55
0=(x+5)( x-11)     doublecheck x*x= x²
5x-11x= -6x
5 * -11= -55
55= (x) (x-6)
5=x-6                 we balance our equation
5+6= x-6+6
11= x                 return to the relationship

width=x Width is 11
length=x-6 Length is 5


Understanding why we take the steps is key to solving for unknowns in an equation. My SPED background includes breaking down mathematical concepts, building critical thinking skills. I looked at the equation, remembered the formula for area, the factors of 55, and immediately noticed that 11-5 equals 6. In my head, I knew the answer in 10 seconds. But, on paper, we break down the steps to build a better understanding of math, a tool we use to maintain our safety with money, time management, and life goals. I was tired, with no calculator, when I took the algebra assessment, so I don't tutor algebra, I just enjoy a challenge. peace

Answer 2

l = w - 6

 

A= lw = (w-6)w = 55

w² - 6w = 55

w² -6w - 55 = 0

(w+5)(w-11) = 0

 

but since the width cannot be -5, the only valid answer is w = 11

l = w - 6 = (11) - 6 = 5