Question

SOMEONE HELP PLS
I need an answer asap the deadline is tomo

Answer 1

Answer: x = 2.5

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Step-by-step explanation:

The rectangle on the left has area of length*width = 4x

The rectangle on the right has an area of x(2x+3) = 2x^2+3x

Combining those two sub areas gets us a total area of 4x+2x^2+3x = 2x^2+7x

Set this equal to the stated area of 30 square mm and get everything to one side.

2x^2+7x = 30

2x^2+7x-30 = 0

Compare this with the template ax^2+bx+c = 0 to find that

• a = 2
• b = 7
• c = -30

We'll plug these values into the quadratic formula like shown below.

`x = (-b\pm√(b^2-4ac))/(2a)\\\\x = (-7\pm√((7)^2-4(2)(-30)))/(2(2))\\\\x = (-7\pm√(49+240))/(4)\\\\x = (-7\pm√(289))/(4)\\\\x = (-7\pm17)/(4)\\\\x = (-7+17)/(4) \ \text{ or } \ x = (-7-17)/(4)\\\\x = (10)/(4) \ \text{ or } \ x = (-24)/(4)\\\\x = (5)/(2) \ \text{ or } \ x = -6\\\\x = 2.5 \ \text{ or } \ x = -6\\\\`

A negative x value doesn't make sense in this context. It's not possible to have a negative length or negative width. So we'll simply ignore x = -6 and go with x = 2.5 as the final answer

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Check:

The rectangle on the left has area of A = 4x = 4*2.5 = 10 square mm.

The rectangle on the right has area B = x*(2x+3) = 2.5*(2*2.5+3) = 20 square mm

The total area is A+B = 10+20 = 30 square mm which matches with what the instructions mentioned. The answer is confirmed.