Y'all i need someone's help rn..

Thanks in advance!

Step-by-step explanation:

Area = length × width

Area = 220 m²

length = width + 12 >from statement The length of the garden is 12m more than its width

By using your solution:

(w +12)w = 220

w¹ × w¹ = w² >add the exponents but make sure they have the same base

w × 12 = 21w

This equation came from the original formula of Area of a rectangle which is AREA = LENGTH × WIDTH.

The problem did not indicated the original dimension for length, instead it specifies that length is 12 m more than its width, thus length = width + 12

Now that we have an expression for length, we are going to substitute length = width + 12 to the original formula of Area

w² + 12w - 220 = 0

This is from: w² + 2w = 220. To achieve this, you take note of the sign of 220, since it is positive, we will have it subtracted from the both sides of the equation to form he standard form of quadratic which is ax² + bx + c = 0

w² + 12w -220 = 220 -220

w² + 12w -220 = 0 >this is now a perfect square

Think of a factor of 220 that when subtracted from each other will have a difference of 12.

In this case the factors are 10 and 22

In sign convension:

Since we have + and -, we will asign tge positive one to the biggest number to yield that positive (bx).

(w + 22)(w - 10) = 0

To find the roots

w + 22 = 0 w - 10 = 0

w + 22 - 22 = -22 w - 10 + 10 = 10

w = -22 w = 10

When we are talking of dimensions, neglect the number with negative sign because there is no such thing as negative length or width.

SOLUTION:

(This is done by using conpleting the square method, if you don't want to find the factors )

Area = length × width

220 = (w + 12) × w >distribute w

220 = w² + 12w >do completing the square

220 + (12/2 •1)² = w² + 12w + (12/2 •1)²

220 + (6)² = w² + 12w + (6)²

220 + 36 = w² + 12w + 36

220 + 36 = (w + 6)² >take the square root of both sides

√(w + 6)² = √(220 + 36)

w + 6 = ± 16

w + 6 - 6 = 16 -6 w + 6 - 6 = -16 -6

w = 10m w = -22m

To find the dimension of length neglect the negative value of w:

Area = length × width

220 = l × 10 >divide both sides by 10 to isolate l

220m²/10m = (l × 10)/10

l = 22 m

Answering the why's:

1. The area is the product of the width and the length,2. Evaluating the quadratic equation.3. Factors are (w + 22) and (w - 10).4. The roots are -22 and 10.5. The length is a distance between two points which is always a positive parameter.6.  We found w = 10, since we said w is the width, it means the width is 10 m.7. w + 12 represents a length. Since w is 10 m, the length is 12 m more, so the length is 10 m + 12m = 22 m.

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Explanation: