Samantha's homework is to determine the dimensions of her rectangular backyard. She knows that the length is 10 feet more than the width, and the total area is 144 square feet. Write an equation that Samantha could use to solve this problem. Then find the dimensions,in feet, of her backyard

Devons homework is the determine the dimensions of his rectangular backyard more than the width and the total area is 144 ft.² find the dimensions in feet of Javins backyard?

In order to determine the dimensions of Samantha's rectangular backyard, we can create an equation based on the given information. Let's assume the width of the backyard is represented by 'x' feet.

Given that the length is 10 feet more than the width, we can express the length as 'x + 10' feet.

The total area of the rectangle is given as 144 square feet. The formula for the area of a rectangle is length multiplied by width.

So, the equation Samantha could use to solve this problem is:

(x + 10) * x = 144

To find the dimensions, we need to solve this equation.

Expanding the equation, we have:

x^2 + 10x = 144

Rearranging the equation to bring all terms to one side:

x^2 + 10x - 144 = 0

Now, we have a quadratic equation, and we can solve it using factoring, completing the square, or the quadratic formula. In this case, we can factor the equation:

(x + 18)(x - 8) = 0

Setting each factor to zero:

x + 18 = 0 or x - 8 = 0

Solving for 'x', we find two possible values:

x = -18 or x = 8

Since we are considering the dimensions of a backyard, a negative value for the width doesn't make sense. Thus, we discard x = -18.

Therefore, the width of Samantha's backyard is 8 feet. And since the length is 10 feet more than the width, the length is:

x + 10 = 8 + 10 = 18 feet

So, the dimensions of Samantha's backyard are 8 feet by 18 feet.

w = width

w + 10 = length
Area = 144

A = Lw
144 = w(w + 10)

Solve for w