the length of a rectangle is 5 centimeters less than three times its width its area is 28 square centimeters find the dimensions of the rectangle

Answer 1

Let's use the variable w to represent the width of the rectangle.

Then we can write the following expression for the length using the info in the problem: (3w - 5)

Since the area of a rectangle is the length times the width, we can write the following equation for the area of this rectangle and use the given 28 square centimeters as the area:

length * width = A

(3w - 5) * (w) = 28

Now we can use the distributive property and solve this equation for feasible values of w:

(3w - 5) * (w) = 28

3w² - 5w = 28

3w² - 5w - 28 = 0

Factor this expression as: (3w + 7) (w-4) = 0

Then setting each factor equal to zero gives us:

3w + 7 = 0

3w + 7 - 7 = 0 -7

3w = -7

w = -7/3 SINCE THE WIDTH CANNOT BE NEGATIVE, THIS IS NOT A POSSIBLE SOLUTION TO USE HERE.

Then w- 4 = 0

w - 4 + 4 = 0 + 4

w = 4

The width of the rectangle is 4 centimeters.

The length will be 3*w - 5 or 3 * 4 - 5 = 7 centimeters

NOTE that the area will be 4 * 7 = 28