A rectangle has a height that is 5 inches less than the base. If the area of the rectangle is 57 inches square, what are the height and base of the rectangle?

The height and base of the rectangle are approximately 5.453 inches and 10.453 inches, respectively.

Step-by-step explanation:

From Geometry we remember that area of a rectangle (), measured in square inches, is equal to:

(Eq. 1)

Where:

- Width, measured in inches.

- Height, measured in inches.

In addition, we get the following relationship from statement:

(Eq. 2)

If we know that , then the height of the rectangle is:

From Quadratic Formula we obtain the following roots:

and

Only the first root offers a reasonable solution, as length has always positive values. Thus, the height of the rectangle is approximately 5.453 inches.

Now we calculate the width of the rectangle from (Eq. 1):

If we know that and , then the width of the rectangle is:

The height and base of the rectangle are approximately 5.453 inches and 10.453 inches, respectively.

the answer is 15% decrease

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.