Answer:
base = 16 cm
height = 7 cm
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