Question

What is the rectangle's height and base?

Answer 1

Answer:

Base = 16cm

Height = 7cm

Answer 2

Answer:

base = 16 cm

height = 7 cm

Step-by-step explanation:

area of a rectangle = base (b) x height (h)

base (b) = 9 + h

area = 112 cm²

plug in values:

112 = (9 + h) * h

112 = 9h + h²

h² + 9h - 112 = 0

h can be solved using quadratic equation

       -9 ± √ (9² - 4 (1) (-112))

h = --------------------------------------

                        2

     -9 ± √529

h = ----------------

            2

h = 7  ;    h = -16

therefore  the height of  a rectangle (h) = 7 cm

solve for base (b)

base (b) = 9 + h

base (b) = 9 + 7

base (b) = 16 cm

proof:

area of a rectangle = base (b) x height (h)

112 = 16 * 7

112 = 112 ---- ok