Answer:
AB = 4.5 cm
Explanation:
the total area (A) of the 2 rectangles is calculated as
A = x(x - 4) + 3x(x - 2)
= x² - 4x + 3x² - 6x
= 4x² - 10x
Given A = 36 , then equating
4x² - 10x = 36 ( subtract 36 from both sides )
4x² - 10x - 36 = 0 ( divide through by 2 )
2x² - 5x - 18 = 0 ← as required
To factorise the equation
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 18 = - 36 and sum = - 5
the factors are + 4 and - 9
use these factors to split the x- term
2x² + 4x - 9x - 18 = 0 ( factor the first/second and third/fourth terms )
2x(x + 2) - 9(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(2x - 9) = 0
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
2x - 9 = 0 ⇒ 2x = 9 ⇒ x = 4.5
but x > 0 , then x = 4.5
Then
AB = x = 4.5 cm