Question

3.

Answer 1

Answer:

x = 5.00 cm

Step-by-step explanation:

• area of the rectangle = $x$   x   $(x + 1)$

                                     = $x^2 + x$

• area of the circle = π r²

                               = $\frac{22}{7}$   x   $(x + 2)^2$

                               = $\frac{22}{7}$   x   $(x^2 + 4x + 4)$

∴   $x^2 + x$   +    $\frac{22}{7}$   x   $(x^2 + 4x + 4) = 184$  

⇒  $x^2 + x$      +   $\frac{22}{7} x^2 \space\ + \space\ \frac{88}{7} x \space\ + \space\ \frac{88}{7} = 184$

⇒  $\frac{29}{7}x^2 \space\ + \space\ \frac{95}{7}x \space\ - \frac{1200}{7} = 0$

• Using quadratic formula, where

a = $\frac{29}{7}$

b = $\frac{95}{7}$

c = $\frac{-1200}{7}$ ,

$x=\frac{-b \pm \sqrt{b^2-4c}}{2}$

$x = \frac{-\frac{95}{7}\pm \sqrt{(\frac{95}{7})^2 - 4(\frac{29}{7})(\frac{-1200}{7} ) } }{2(\frac{29}{7})}$

$x = 5.00 \space\ \space\ \space\ or \space\ \space\ \space\ x = -8.28$

As length (x) cannot be a negative number,

x = 5.00 cm