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.