Chapter 6.2, Problem 51E

To determine

To select: the correct value of b in terms of p from the given options.

Answer to Problem 51E

  $\text{D}$

Explanation of Solution

Given information:

The figure of rectangle is shown below.

  

Perimeter of rectangle $=p$

  $a=\frac{3}{4}b$

The options given are as follows:

  $\begin{array}{l}\text{A }\frac{p}{7}\\ \text{B }\frac{4p}{7}\\ \text{C }\frac{7}{p}\\ \text{D }\frac{2p}{7}\\ \text{E }\frac{7p}{4}\end{array}$

Calculation:

The perimeter of the rectangle $QRTS$ is evaluated as follows:

  $\begin{array}{c}p=2a+2b\\ =2\left(\frac{3}{4}b\right)+2b\left[\text{Put the value of }a\text{ and }b\right]\\ =\frac{3}{2}b+2b\\ p=\frac{7}{2}b\\ b=\frac{2p}{7}\end{array}$

Thus option D is correct.