The dimensions of a rectangle is 30cm x 20cm. When each dimension is decreased by the same amount, the area of the new rectangle is
100cm^2. What are the new dimensions of the new rectangle (round to
one decimal place)? Hint: you will need to use the quadratic equation.

The new dimensions are 6.18 cm by 16.18 cm.

Step-by-step explanation:

Original dimensions were 30 cm by 20 cm.

We decrease length and width by x and calculate the area:

Area = (length)(width)

        = (30 - x)(20 - x) = 100

Performing the indicated multiplication, we get:

600 - 30x - 20x + x^2 = 100, or, after simplification,

x^2 - 50x + 500 = 0

Let's solve this by completing the square:

x^2 - 50x + 500 = x^2 - 50x + 625 - 625 + 500 = 0

This simplifies to (x - 25)^2 - 125 = 0, or (x - 25)^2 = 125

Taking the square root of both sides, we get:

x - 25 = ±√125, or

x = 25 ± 5√5

The two results are x = 36.18 (not possible, because we DECREASED the original dimensions) and x = 13.82 (possible)

The dimensions of the new rectangle are

(30 - 13.82) cm by (20 - 13.82) cm, or

16.2 cm by 6.18 cm

Check:  With these dimensions is the area 100 cm^2, as expected?

(6.18)(16.18) = 99.9979    YES

step-by-step explanation:

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.