Question

Azeyah wants to buy a wooden rod to install curtains on the window of his room. The area of the window is ( 4x²+2x-12 ) cm². If the window's height is ( 2x+4 ) cm, what is the length, in cm, of the wooden rod required?

Pls help ASAP ​

Answer 1

(2x-3)cm

Answer:

Solution given:

height =2x+4

length=?

Area of window =(4x²+2x-12)cm²

we have

length*height =Area

length*(2x+4)=4x²+2x-12......(1)

Firstly let factorize 4x²+2x-12

taking common 2(2x²+x-6)

doing middle term factorization 2(2x²+4x-3x-6)

=2(2x(x+2)-3(x+2))

=2(x+2)(2x-3)

substituting it in equation 1

length*(2x+4)=2(x+2)(2x-3)

length*2(x+2)=2(x+2)(2x-3)

length =2x-3 cm

The length of window is (2x-3)cm

Answer 2

(2x - 3) cm

Explanation:

Area of window = height × length

Given:

• Area = (4x² + 2x - 12) cm²
• Height = (2x + 4) cm

To find the length of the window, factor the expression for Area.

Factor
`4x^2+2x-12`:

Find 2 two numbers that multiply to the product of the leading coefficient and the constant (4 × -12 = -48) and sum to the coefficient of the middle term (2): -6 and 8

Rewrite the middle term as the sum of these 2 numbers:

`\implies 4x^2-6x+8x-12`

Factorize the first two terms and the last two terms separately:

`\implies 2x(2x-3)+4(2x-3)`

Factor out the common term (2x - 3):

`\implies (2x+4)(2x-3)`

Therefore, the length of the window is (2x - 3) cm