Chapter 76, Problem 1A

To determine

To find the length of the diagonal $AB$.

Answer to Problem 1A

  $AB=9.56\text{ inch}$.

Explanation of Solution

Given information:

We are given the following figure-

  

Calculation:

After observing the figure closely and then writing the relation to calculate the length of diagonal $AB$.

  $\begin{array}{l}A{B}^2=A{C}^2+B{C}^2\mathrm{....}\text{(1)}\text{{}\because ACB\text{ is a right triangle right angled at C}}\\ \text{calculate the value of }B{C}^2\\ B{C}^2={(}^{8.25}+{(}^{4.5}\\ BC=\sqrt{{(8.25)}^2+{(4.5)}^2}\\ BC=\sqrt{68.0625+20.25}\\ BC=\sqrt{88.3125}\\ BC=9.4\text{ inch}\end{array}$

  $\begin{array}{l}A{B}^2=A{C}^2+B{C}^2\mathrm{....}\text{(1)}\\ \text{Now substitute }AC=1.75\text{ and }BC=9.4\text{ in (1)}\\ AB=\sqrt{A{C}^2+B{C}^2}\\ AB=\sqrt{{(1.75)}^2+{(9.4)}^2}\\ AB=\sqrt{3.0625+88.3125}\\ AB=\sqrt{91.375}\\ AB=9.56\text{ inch}\end{array}$