The length of a rectangle exceeds its width by 7 inches and the area is 30 square inches. what are the length and width of the rectangle?

Let's assume w represent the width of the rectangle.

Given that, the length of a rectangle exceeds its width by 7 inches. So,

length = w + 7.

Given, area is 30 square inches.

Since Area = l * w

So, we can set up an equation as following:

(w + 7) * w = 30

w² + 7w = 30 By distribution property.

w² + 7w - 30 = 0 Subtract 30 from each sides.

Next step is to solve the above equation by factoring to get the value of w.

First step is to breakdown the constant - 30 into two multiples so that their addition will result the coefficient of w = 7.

So, - 30 = - 3 * 10.

Addition of - 3 and 10 will give 7.

So, next step is to replace 7w with - 3w + 10w. Therefore,

w² - 3w + 10w - 30 = 0

(w² - 3w) + (10w - 30) = 0 Make the group of terms.

w (w - 3) + 10 (w - 3) = 0 Take out the common factor from each group.

(w - 3) (w + 10) = 0 Take out the common factor (w - 3).

w - 3 = 0 and w + 10 = 0 Set up each factor equal to 0.

So, w = 3 and - 10.

Width cannot be negative 10.

So, w = 3.

Now length = w + 7 = 3 + 7 = 10

Hence length of the rectangle is 10 inches and width is 3 inches.