Answer:
length = 6 cm , breadth = 4 cm
Explanation:
the area (A) of the large rectangle = length × breadth
here length = 12 cm and breadth = 4 + x , then
A = 12(4 + x) cm²
the area (A) of the smaller rectangle = x(x + 2)
given area of larger is 4 times area of smaller then
12(x + 4) = 4x(x + 2) ← distribute parenthesis on both sides
12x + 48 = 4x² + 8x , that is
4x² + 8x = 12x + 48 ( subtract 12x + 48 from both sides )
4x² - 4x - 48 = 0 ( divide through by 4 )
x² - x - 12 = 0 ← in standard form
(x - 4)(x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 3 = 0 ⇒ x = - 3
but x must be greater than zero, so x = 4
dimensions of smaller rectangle are
length = x + 2 = 4 + 2 = 6 cm
breadth = x = 4 cm