Question

The area of a rectangle is 28x6y9 square feet. If the length of the rectangle is 14x3y3 feet, which expression represents the width of the rectangle?

Answer 1

W = 2*x^3*y^6

Explanation:

For this problem, we need to use the relationship:

a^x/a^y = a^(x - y)

For a rectangle with length L and width W, the area is:

A = L*W

We know that in this case we have:

A = 28*x^6*y^9

and:

L = 14*x^3*y^3

We want to find the value of W.

Using the above equation, we have that:

A = 28*x^6*y^9 = L*W = (14*x^3*y^3)*W

28*x^6*y^9 = (14*x^3*y^3)*W

We can solve this for W by isolating it in the right side.

First, let's divide by 14 in both sides to get:

(28*x^6*y^9)/14 = (14*x^3*y^3)*W/14

(28/14)*x^6*y^9 = (14/14)*x^3*y^3*W

2*x^6*y^9 = x^3*y^3*W

Now let's divide by x^3 in both sides to get:

(2*x^6*y^9)/x^3 = (x^3*y^3*W)/x^3

2*(x^6/x^3)*y^9 = (x^3/x^3)*y^3*W

Now we use the relationship that is in the beginning:

2*x^(6 - 3)*y^9 = y^3*W

2*x^3*y^9 = y^3*W

Now let's divide by y^3 in both sides:

(2*x^3*y^9)/y^3 = (y^3*W)/y^3

2*x^3(y^9/y^3) = (y^3/y^3)*W

2*x^3*y^(9 - 3) = W

2*x^3*y^6 = W

The width of the rectangle is given by the equation:

W = 2*x^3*y^6

Answer 2

2x³y⁶

Explanation:

A rectangle is a plan shape with pair of opposite side equal and parallel.

The Area of a rectangle is

A = L×W ........................... Equation 1

Where L = Length, W = Width.

make W the subject of the equation.

W = A/L.................... Equation 2

Given: A = 28x⁶y⁹ square feet, L = 14x³y³ feet.

Substitute into equation 2

W = 28x⁶y⁹/14x³y³

W = 2x³y⁶ feet.

Hence the expreesion for the width is 2x³y⁶