Chapter 11.2, Problem 19PPS

To determine

To find: The length of the diagonal.

Answer to Problem 19PPS

The two diagonals are of $31.0\text{in}$ and $15.5\text{in}$ .

Explanation of Solution

Given:

The area of the rhombus is $168{\text{cm}}^2$ .

The size of one diagonal is three times the other.

Calculation:

Consider the diagonal of the kite is thrice as long as the other diagonal then,

  $d_1=3d_2$

Then, the area of the kite is obtained as,

  $\begin{array}{l}A=\frac{d_1{d}_2}{2}\\ 168{\text{cm}}^2=\frac{3d_2{d}_2}{2}\\ d_2^2=\frac{2}{3}\left(168{\text{cm}}^2\right)\\ d_2=10.6\text{cm}\end{array}$

Then, the other diagonal is obtained as,

  $\begin{array}{c}{d}_1=3\left(10.6\text{cm}\right)\\ =31.7\text{cm}\end{array}$

Thus, the two diagonals are of $10.6\text{cm}$ and $31.7\text{cm}$ .