Chapter 14.6, Problem 21PPS

To determine

To calculate area of base of given figure.

Answer to Problem 21PPS

5 units

Explanation of Solution

Given information:

volume of cuboid= $3x^3+6x^2-30x$

height= $3x$

base= $x$

Formula used :volume of cuboid = length×breadth×height

Calculation:

According to question,

Volume of cuboid= length×breadth×height

Base of cuboid is square

Length =breadth

Now,

Volume of cuboid is= $3x^3+6x^2-30x$

length×breadth×height= $3x^3+6x^2-30x$

  $x\times x\times 3x$ = $3x^3+6x^2-30x$

  $\begin{array}{l}x\times x\times 3x=3x^3+6x^2-30x\\ 3x^3=3x^3+6x^2-30x\\ 0=3x^3+6x^2-30x-3x^3\\ 0=6x^2-30\\ 6x^2=30\\ x^2=5\end{array}$

Now we know that area of base is base×length (because it is square)

  $x^2=5$

Hence, area of square base is,

5 units