Chapter 7.4, Problem 70PPE

To determine

To find: the area of the rectangle is $72a^3{b}^4$ . What is the length of the rectangle?

  

Answer to Problem 70PPE

The required answer is: length of the rectangle is $12a^2{b}^3$

Explanation of Solution

Given information:

The given information: area of the rectangle is $72a^3{b}^4$ and breadth is 6ab

Calculation:

Area of rectangle $=72a^3{b}^4$

  $l\times b=72a^3{b}^4$

(Since Area of rectangle $=l\times b$ )

  $l\times 6ab=72a^3{b}^4$

(Given breadth is 6ab)

  $l\times \frac{6ab}{6ab}=\frac{72a^3{b}^4}{6ab}$

(Divide 6ab on both sides)

  $\begin{array}{l}l=\frac{72a^3{b}^4}{6ab}\\ l=\frac{72}{6}{a}^{3-1}{b}^{4-1}\end{array}$

(Subtract exponents when dividing powers with the same base)

  $l=12a^2{b}^3$

(Simplify)

Therefore the length of the rectangle is $12a^2{b}^3$