Question

What is the breadth of a rectangular park with $15x^6{z}^5$ unit${}^2$ area and length $5x^3{z}^4$ units?

• A. $3x^3{z}^4$
• B. $3x^{3}z$
• C. $3x^4{z}^3$
• D. None of the above

Answer 1

The correct option is B $3x^{3}z$

Given:
$\bullet$ Area of rectangular park $=15x^6{z}^5\text{unit}{}^2$
$\bullet$ Length of rectangular park $=5x^3{z}^4$ units

As per the hint,
Area of rectangle $=$ Length $\times$ Breadth

$⟹15x^6{z}^5=5x^3{z}^4\times$ Breadth

$⟹\frac{15x^6{z}^5}{5x^3{z}^4}=\frac{5x^3{z}^4\times \text{Breadth}}{5x^3{z}^4}$

$⟹$ Breadth $=\frac{15x^6{z}^5}{5x^3{z}^4}$

$⟹$ Breadth $=(\frac{15}{5})x^{6-3}{z}^{5-4}$
[ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Division rule of exponents: $\frac{a^m}{a^n}=a^{m-n}$ ]

$⟹$ Breadth $=3x^{3}z$

$\therefore$ The breadth of the rectangular park is $3x^{3}z$ units.

Therefore, option (b.) is the correct one.