Question

what is the length of a rectangle with an area of (4x2+12x) square units if the width is 4x units

Answer 1

Answer:

The area of a rectangle is 6x^2 + 5x – 6, and its width is 3x – 2. What is the length of the rectangle?

Area of rectangle = 6x2+5x−6

Width = 3x−2

In area equation, multiply coefficient of first term with third term, which is constant and find factors.

6×(−6)=−36 ⟹ −1×2×2×3×3=−36

Now check for middle term and try to find out whether addition or subtraction of factors equals to coefficient of middle term or not?

(3×3)+(−1×2×2)=9−4=5 ✓

Yes this equation can be factored.

(6x+9)(6x−4)

First bracket is divisible by 3 and second is divisible by 2 , so simplify it.

(2x+3)(3x−2)

One of the factors (3x−2) of this equation is equal to width of rectangle, so division results into,

(2x+3) and that's the length of rectangular

I hope it's help you