Question

***WILL MAKE BRAINLIEST***

Answer 1

The value of x is 3.

Solution:

Length of the top rectangle = x ft

Width of the top rectangle = x ft

Height of the top rectangle = 3x ft

Volume of the top rectangle $=x \times x\times 3x$

                                               $=3x^{1+1+1}$

Volume of the top rectangle $=3x^3$ cubic feet

Length of the bottom rectangle = $x\sqrt{2}$ ft

Width of the bottom rectangle = $x\sqrt{2}$ ft

Height of the bottom rectangle = 0.5 ft

Volume of the bottom rectangle $=x\sqrt{2} \times x\sqrt{2} \times 0.5$

                                                      $=2x^{1+1}\times 0.5$

Volume of the bottom rectangle $=x^2$ cubic feet

Total concrete for both pieces = 90 cubic feet.

Volume of top + volume of bottom = 90 cubic feet

$3 x^{3}+x^{2}=90$

$3 x^{3}+x^{2}-90=0$

Solve by factoring.

$(x-3)\left(3 x^{2}+10 x+30\right)=0$

x = 3, $\left(3 x^{2}+10 x+30\right)=0$

Solve using quadratic formula,

$x=3, x=-\frac{5}{3}+i \frac{\sqrt{65}}{3}, x=-\frac{5}{3}-i \frac{\sqrt{65}}{3}$

Ignore the complex roots.

The value of x is 3.