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please help me work this out! set up and solve a quadratic equation to work out the value of x

Please Help Me Work This Out Set Up And Solve A Quadratic Equation To Work Out The Value Of X class=

Sagot :

akposevictor

Answer:

x = 8

Step-by-step explanation:

✔️Area of the square = s²

Where,

s = (2x - 4)

Area = (2x - 4)² = (2x - 4)(2x - 4) = 2x(2x - 4) -4(2x - 4)

= 4x² - 8x - 8x + 16

Area of square = 4x² - 16x + 16

Area of rectangle = L × W = (3x - 6) × x

= 3x² - 6x

✔️Since both have the same area, therefore,

4x² - 16x + 16 = 3x² - 6x

Collect like terms

4x² - 3x² - 16x + 6x + 16 = 0

x² - 10x + 16 = 0

Factorize

x² - 2x - 8x + 16 = 0

x(x - 2) -8(x - 2) = 0

(x - 2)(x - 8) = 0

(x - 2) = 0 or (x - 8) = 0

x = 2 or x = 8

If we plug in x = 2 into any of the given side length, we would have 0. (i.e. 2x - 4 = 2*2 - 4 = 0)

So the value of x cannot be 2 because the length of any of the shape cannot be 0.

So therefore, the value of x = 8

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