Plz help what does the last question in part b mean?
It's ex 3
Answers
Step-by-step explanation:
hope this will help u a lot
Given:
- Side of the square(ABCD) = 3x-1
- Legth of the rectangle(CEFG) = 3x-1
- Breadth of the rectangle(CEFG) = x+2
- Area of square ABCD is equal to Area of rectangle CEFG.
To find:
- Value of x
Solution:
Now, we know that:
⇒Area of Square = (Side)²
⇒Area of rectangle = Length×Breadth
We know that the area of square ABCD is equal to area of rectangle CEFG. This implies that:
⇒Area of square = Area of rectangle
⇒(Side)² = Length×Breadth
Let us apply the given values in the formula.
⇒(Side)² = Length×Breadth
⇒(3x-1)² = (3x-1)(x+2)
Let us consider the left hand side. In left hand side, we are going to use an identity: (a-b)²=a²+b²-2ab. By applying this identity in Left hand side, we will get:
⇒(3x-1)² = (3x)²+(1)²-2×3x×1
⇒9x²+1-6x
Let us apply the acquired value in the actual equation:
⇒(3x-1)² = (3x-1)(x+2)
⇒9x²+1-6x = (3x)×(x)+(3x)×2+(-1)×(x)+(-1)×2
⇒9x²+1-6x = 3x²+6x-x-2
⇒9x²+1-6x = 3x²+5x-2
Now, our problem is half-completed. Now, it is easier to cancel and find the value of x:
⇒9x²+1-6x = 3x²+5x-2
⇒9x²-3x²+1-6x = 5x-2
⇒6x²+1-6x = 5x-2
⇒6x²+1-6x-5x = -2
⇒6x²+1-11x = -2
⇒6x²-11x+1+2 = 0
⇒6x²-11x+3 = 0
Now, we arrived a quadratic equation. Here, we will split the middle term by factorization method.
⇒6x²-11x+3 = 0
- Here, -11x can be written as (-2x)-(9x). This process is called splitting of middle term.
⇒6x²-2x-9x+3 = 0
- Let us take 2x and -3 as common factors from this equation.
⇒2x(3x-1)-3(3x-1) = 0
- Further, let us write the equation in factored form.
⇒(2x-3)(3x-1) = 0
⇒2x-3 = 0 or 3x-1 = 0
⇒2x = 3 or 3x = 1
⇒x = 3/2 or 1/3
- Thus, we have arrived two values of x. Both the values satisfy for your given question.
On arriving the last statement,
- The value of x is either 3/2 or 1/3.